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Link de la búsquedaApproximation and Computation / SpringerLink (Online service) ; Walter Gautschi ; Giuseppe Mastroianni ; Rassias, Themistocles M (2011)
Título : Approximation and Computation : In Honor of Gradimir V. Milovanovic Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Walter Gautschi ; Giuseppe Mastroianni ; Rassias, Themistocles M Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Springer Optimization and Its Applications, ISSN 1931-6828 num. 42 Número de páginas: XVIII, 482 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-6594-3 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Approximation theory mathematics Mathematical optimization Optimization Computational and Numerical Analysis Approximations Expansions of Computing Clasificación: 51 Matemáticas Resumen: Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanovic, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences Nota de contenido: Part I Introduction. -- The Scientific Work of Gradimir V. Milovanovic (Aleksandar Ivic) -- My Collaboration with Gradimir V. Milovanovic (Walter Gautschi) -- On Some Major Trends in Mathematics (Themistocles M. Rassias) -- Part II Polynomials and Orthogonal Systems -- An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant (Paul Barry, Predrag M. Rajkovic and Marko D. Petkovic) -- Extremal Problems for Polynomials in the Complex Plane (Borislav Bojanov) -- Energy of Graphs and OrthogonalMatrices (V. Božin and M. Mateljevic) -- Interlacing Property of Zeros of Shifted Jacobi Polynomials (Aleksandar S. Cvetkovic) -- Trigonometric Orthogonal Systems (Aleksandar S. Cvetkovic and Marija P. Stanic) -- Experimental Mathematics Involving Orthogonal Polynomials (Walter Gautschi) -- Compatibility of Continued Fraction Convergents with Padé Approximants (Jacek Gilewicz and Radoslaw Jedynak) -- Orthogonal Decomposition of Fractal Sets (Ljubiša M. Kocic, Sonja Gegovska Zajkova, Elena Babace) -- Positive Trigonometric Sums and Starlike Functions (Stamatis Koumandos) -- Part III Quadrature Formulae. -- Quadrature Rules for Unbounded Intervals and Their Application to Integral Equations (G. Monegato, L. Scuderi) -- GaussType Quadrature Formulae for Parabolic Splines with Equidistant Knots (Geno Nikolov and Corina Simian) -- Approximation of the Hilbert Transform on the Real Line Using Freud Weights (Incoronata Notarangelo) -- The Remainder Term of GaussTur´an Quadratures for Analytic Functions (Miodrag M. Spalevic and Miroslav S. Pranic) -- Towards a General Error Theory of the Trapezoidal Rule (Jörg Waldvogel) -- Part IV Differential Equations -- Finite Difference Method for a Parabolic Problem with Concentrated Capacity and TimeDependent Operator (Dejan R. Bojovic and Boško S. Jovanovic) -- Adaptive Finite Element Approximation of the FrancfortMarigo Model of Brittle Fracture (Siobhan Burke, Christoph Ortner and Endre Süli) -- A NyströmMethod for Solving a Boundary Value Problems on [0, 8) (Carmelina Frammartino) -- Finite Difference Approximation of a Hyperbolic Transmission Problem (Boško S. Jovanovic) -- Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of AProper Maps with Applications (P. S. Milojevic) -- Singular Support and FLq Continuity of Pseudodifferential Operators (Stevan Pilipovic, Nenad Teofanov and Joachim Toft) -- On a Class of Matrix Differential Equations with Polynomial Coefficients (Boro M. Piperevski) -- Part V Applications -- Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices (Raka Jovanovic and Milan Tuba) -- Explicit Method for the Numerical Solution of the FokkerPlanck Equation of Filtered Phase Noise (Dejan Milic) -- Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to GravityInduced Skeletal Settling (Zoran S. Nikolic) -- Computer Algebra and Line Search (Predrag Stanimirovic, Marko Miladinovic and Ivan M. Jovanovic) -- Roots of AGbands (Nebojša Stevanovic and Petar V. Protic) -- Context Hidden MarkovModel for Named Entity Recognition (Branimir T. Todorovic, Svetozar R. Rancic, Edin H. Mulalic) -- On the Interpolating Quadratic Spline (Zlatko Udovicic) -- Visualization of Infinitesimal Bending of Curves (Ljubica S. Velimirovic, Svetozar R. Rancic, Milan Lj. Zlatanovic) En línea: http://dx.doi.org/10.1007/978-1-4419-6594-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33147 Approximation and Computation : In Honor of Gradimir V. Milovanovic [documento electrónico] / SpringerLink (Online service) ; Walter Gautschi ; Giuseppe Mastroianni ; Rassias, Themistocles M . - New York, NY : Springer New York, 2011 . - XVIII, 482 p : online resource. - (Springer Optimization and Its Applications, ISSN 1931-6828; 42) .
ISBN : 978-1-4419-6594-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Approximation theory mathematics Mathematical optimization Optimization Computational and Numerical Analysis Approximations Expansions of Computing Clasificación: 51 Matemáticas Resumen: Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to the renowned mathematician Gradimir V. Milovanovic, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines. - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in engineering and other computational and applied sciences Nota de contenido: Part I Introduction. -- The Scientific Work of Gradimir V. Milovanovic (Aleksandar Ivic) -- My Collaboration with Gradimir V. Milovanovic (Walter Gautschi) -- On Some Major Trends in Mathematics (Themistocles M. Rassias) -- Part II Polynomials and Orthogonal Systems -- An Application of Sobolev Orthogonal Polynomials to the Computation of a Special Hankel Determinant (Paul Barry, Predrag M. Rajkovic and Marko D. Petkovic) -- Extremal Problems for Polynomials in the Complex Plane (Borislav Bojanov) -- Energy of Graphs and OrthogonalMatrices (V. Božin and M. Mateljevic) -- Interlacing Property of Zeros of Shifted Jacobi Polynomials (Aleksandar S. Cvetkovic) -- Trigonometric Orthogonal Systems (Aleksandar S. Cvetkovic and Marija P. Stanic) -- Experimental Mathematics Involving Orthogonal Polynomials (Walter Gautschi) -- Compatibility of Continued Fraction Convergents with Padé Approximants (Jacek Gilewicz and Radoslaw Jedynak) -- Orthogonal Decomposition of Fractal Sets (Ljubiša M. Kocic, Sonja Gegovska Zajkova, Elena Babace) -- Positive Trigonometric Sums and Starlike Functions (Stamatis Koumandos) -- Part III Quadrature Formulae. -- Quadrature Rules for Unbounded Intervals and Their Application to Integral Equations (G. Monegato, L. Scuderi) -- GaussType Quadrature Formulae for Parabolic Splines with Equidistant Knots (Geno Nikolov and Corina Simian) -- Approximation of the Hilbert Transform on the Real Line Using Freud Weights (Incoronata Notarangelo) -- The Remainder Term of GaussTur´an Quadratures for Analytic Functions (Miodrag M. Spalevic and Miroslav S. Pranic) -- Towards a General Error Theory of the Trapezoidal Rule (Jörg Waldvogel) -- Part IV Differential Equations -- Finite Difference Method for a Parabolic Problem with Concentrated Capacity and TimeDependent Operator (Dejan R. Bojovic and Boško S. Jovanovic) -- Adaptive Finite Element Approximation of the FrancfortMarigo Model of Brittle Fracture (Siobhan Burke, Christoph Ortner and Endre Süli) -- A NyströmMethod for Solving a Boundary Value Problems on [0, 8) (Carmelina Frammartino) -- Finite Difference Approximation of a Hyperbolic Transmission Problem (Boško S. Jovanovic) -- Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of AProper Maps with Applications (P. S. Milojevic) -- Singular Support and FLq Continuity of Pseudodifferential Operators (Stevan Pilipovic, Nenad Teofanov and Joachim Toft) -- On a Class of Matrix Differential Equations with Polynomial Coefficients (Boro M. Piperevski) -- Part V Applications -- Optimized Algorithm for Petviashvili’s Method for Finding Solitons in Photonic Lattices (Raka Jovanovic and Milan Tuba) -- Explicit Method for the Numerical Solution of the FokkerPlanck Equation of Filtered Phase Noise (Dejan Milic) -- Numerical Method for Computer Study of Liquid Phase Sintering: Densification Due to GravityInduced Skeletal Settling (Zoran S. Nikolic) -- Computer Algebra and Line Search (Predrag Stanimirovic, Marko Miladinovic and Ivan M. Jovanovic) -- Roots of AGbands (Nebojša Stevanovic and Petar V. Protic) -- Context Hidden MarkovModel for Named Entity Recognition (Branimir T. Todorovic, Svetozar R. Rancic, Edin H. Mulalic) -- On the Interpolating Quadratic Spline (Zlatko Udovicic) -- Visualization of Infinitesimal Bending of Curves (Ljubica S. Velimirovic, Svetozar R. Rancic, Milan Lj. Zlatanovic) En línea: http://dx.doi.org/10.1007/978-1-4419-6594-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33147 Ejemplares
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Título : Approximation Algorithms for Complex Systems : Proceedings of the 6th International Conference on Algorithms for Approximation, Ambleside, UK, 31st August - 4th September 2009 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Emmanuil H. Georgoulis ; Armin Iske ; Jeremy Levesley Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: Springer Proceedings in Mathematics, ISSN 2190-5614 num. 3 Número de páginas: X, 310 p Il.: online resource ISBN/ISSN/DL: 978-3-642-16876-5 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Applied mathematics Engineering Computer Algorithms Numerical analysis Approximations and Expansions Computational Analysis Science Applications of Clasificación: 51 Matemáticas Resumen: This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom Nota de contenido: Part I INVITED SURVEYS: Emergent Behaviour in Large Electrical Networks -- Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation -- Anisotropic Triangulation Methods in Adaptive Image Approximation -- Form Assessment in Coordinate Metrology -- Discontinuous Galerkin Methods for Linear Problems: An Introduction -- A Numerical Analyst’s View of the Lattice Boltzmann Method -- Approximating Probability Measures on Manifolds via Radial Basis Functions -- Part II CONTRIBUTED RESEARCH PAPERS: Modelling Clinical Decay Data Using Exponential Functions -- Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions -- Stabilizing Lattice Boltzmann Simulation of Fluid Flow past a Circular Cylinder with Ehrenfests’ Limiter -- Fast and Stable Interpolation of Well Data Using the Norm Function -- Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data -- On Bivariate Interpolatory Mask Symbols, Subdivision and Re?nable Functions -- Model and Feature Selection in Metrology Data Approximation En línea: http://dx.doi.org/10.1007/978-3-642-16876-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33399 Approximation Algorithms for Complex Systems : Proceedings of the 6th International Conference on Algorithms for Approximation, Ambleside, UK, 31st August - 4th September 2009 [documento electrónico] / SpringerLink (Online service) ; Emmanuil H. Georgoulis ; Armin Iske ; Jeremy Levesley . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - X, 310 p : online resource. - (Springer Proceedings in Mathematics, ISSN 2190-5614; 3) .
ISBN : 978-3-642-16876-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Applied mathematics Engineering Computer Algorithms Numerical analysis Approximations and Expansions Computational Analysis Science Applications of Clasificación: 51 Matemáticas Resumen: This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom Nota de contenido: Part I INVITED SURVEYS: Emergent Behaviour in Large Electrical Networks -- Algorithms and Error Bounds for Multivariate Piecewise Constant Approximation -- Anisotropic Triangulation Methods in Adaptive Image Approximation -- Form Assessment in Coordinate Metrology -- Discontinuous Galerkin Methods for Linear Problems: An Introduction -- A Numerical Analyst’s View of the Lattice Boltzmann Method -- Approximating Probability Measures on Manifolds via Radial Basis Functions -- Part II CONTRIBUTED RESEARCH PAPERS: Modelling Clinical Decay Data Using Exponential Functions -- Towards Calculating the Basin of Attraction of Non-Smooth Dynamical Systems Using Radial Basis Functions -- Stabilizing Lattice Boltzmann Simulation of Fluid Flow past a Circular Cylinder with Ehrenfests’ Limiter -- Fast and Stable Interpolation of Well Data Using the Norm Function -- Algorithms and Literate Programs for Weighted Low-Rank Approximation with Missing Data -- On Bivariate Interpolatory Mask Symbols, Subdivision and Re?nable Functions -- Model and Feature Selection in Metrology Data Approximation En línea: http://dx.doi.org/10.1007/978-3-642-16876-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33399 Ejemplares
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Título : Approximation Theory and Harmonic Analysis on Spheres and Balls Tipo de documento: documento electrónico Autores: Feng Dai ; SpringerLink (Online service) ; Yuan Xu Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XVIII, 440 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-6660-4 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Fourier Special functions Approximations and Expansions Functions Clasificación: 51 Matemáticas Resumen: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area Nota de contenido: 1 Spherical Harmonics -- 2 Convolution and Spherical Harmonic Expansion -- 3 Littlewood-Paley Theory and Multiplier Theorem -- 4 Approximation on the Sphere -- 5 Weighted Polynomial Inequalities -- 6 Cubature Formulas on Spheres -- 7 Harmonic Analysis Associated to Reflection Groups -- 8 Boundedness of Projection Operator and Cesàro Means -- 9 Projection Operators and Cesàro Means in L^p Spaces -- 10 Weighted Best Approximation by Polynomials -- 11 Harmonic Analysis on the Unit Ball -- 12 Polynomial Approximation on the Unit Ball -- 13 Harmonic Analysis on the Simplex -- 14 Applications -- A Distance, Difference and Integral Formulas -- B Jacobi and Related Orthogonal Polynomials -- References -- Index -- Symbol Index En línea: http://dx.doi.org/10.1007/978-1-4614-6660-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32314 Approximation Theory and Harmonic Analysis on Spheres and Balls [documento electrónico] / Feng Dai ; SpringerLink (Online service) ; Yuan Xu . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XVIII, 440 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-1-4614-6660-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Approximation theory Fourier Special functions Approximations and Expansions Functions Clasificación: 51 Matemáticas Resumen: This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area Nota de contenido: 1 Spherical Harmonics -- 2 Convolution and Spherical Harmonic Expansion -- 3 Littlewood-Paley Theory and Multiplier Theorem -- 4 Approximation on the Sphere -- 5 Weighted Polynomial Inequalities -- 6 Cubature Formulas on Spheres -- 7 Harmonic Analysis Associated to Reflection Groups -- 8 Boundedness of Projection Operator and Cesàro Means -- 9 Projection Operators and Cesàro Means in L^p Spaces -- 10 Weighted Best Approximation by Polynomials -- 11 Harmonic Analysis on the Unit Ball -- 12 Polynomial Approximation on the Unit Ball -- 13 Harmonic Analysis on the Simplex -- 14 Applications -- A Distance, Difference and Integral Formulas -- B Jacobi and Related Orthogonal Polynomials -- References -- Index -- Symbol Index En línea: http://dx.doi.org/10.1007/978-1-4614-6660-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32314 Ejemplares
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Título : Approximation Theory : From Taylor Polynomials to Wavelets Tipo de documento: documento electrónico Autores: Ole Christensen ; SpringerLink (Online service) ; Khadija L. Christensen Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Otro editor: Imprint: Birkhäuser Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XI, 156 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4448-2 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Applied mathematics Engineering Analysis Approximations and Expansions Abstract Applications of Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas Nota de contenido: 1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References En línea: http://dx.doi.org/10.1007/978-0-8176-4448-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35195 Approximation Theory : From Taylor Polynomials to Wavelets [documento electrónico] / Ole Christensen ; SpringerLink (Online service) ; Khadija L. Christensen . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2005 . - XI, 156 p. 5 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4448-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Applied mathematics Engineering Analysis Approximations and Expansions Abstract Applications of Signal, Image Speech Processing Clasificación: 51 Matemáticas Resumen: This concisely written book gives an elementary introduction to a classical area of mathematics—approximation theory—in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Key features and topics: * Description of wavelets in words rather than mathematical symbols * Elementary introduction to approximation using polynomials (Weierstrass’ and Taylor’s theorems) * Introduction to infinite series, with emphasis on approximation-theoretic aspects * Introduction to Fourier analysis * Numerous classical, illustrative examples and constructions * Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints * Minimal prerequisites: elementary calculus * Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas Nota de contenido: 1 Approximation with Polynomials -- 1.1 Approximation of a function on an interval -- 1.2 Weierstrass’ theorem -- 1.3 Taylor’s theorem -- 1.4 Exercises -- 2 Infinite Series -- 2.1 Infinite series of numbers -- 2.2 Estimating the sum of an infinite series -- 2.3 Geometric series -- 2.4 Power series -- 2.5 General infinite sums of functions -- 2.6 Uniform convergence -- 2.7 Signal transmission -- 2.8 Exercises -- 3 Fourier Analysis -- 3.1 Fourier series -- 3.2 Fourier’s theorem and approximation -- 3.3 Fourier series and signal analysis -- 3.4 Fourier series and Hilbert spaces -- 3.5 Fourier series in complex form -- 3.6 Parseval’s theorem -- 3.7 Regularity and decay of the Fourier coefficients -- 3.8 Best N-term approximation -- 3.9 The Fourier transform -- 3.10 Exercises -- 4 Wavelets and Applications -- 4.1 About wavelet systems -- 4.2 Wavelets and signal processing -- 4.3 Wavelets and fingerprints -- 4.4 Wavelet packets -- 4.5 Alternatives to wavelets: Gabor systems -- 4.6 Exercises -- 5 Wavelets and their Mathematical Properties -- 5.1 Wavelets and L2 (?) -- 5.2 Multiresolution analysis -- 5.3 The role of the Fourier transform -- 5.4 The Haar wavelet -- 5.5 The role of compact support -- 5.6 Wavelets and singularities -- 5.7 Best N-term approximation -- 5.8 Frames -- 5.9 Gabor systems -- 5.10 Exercises -- Appendix A -- A.1 Definitions and notation -- A.2 Proof of Weierstrass’ theorem -- A.3 Proof of Taylor’s theorem -- A.4 Infinite series -- A.5 Proof of Theorem 3 7 2 -- Appendix B -- B.1 Power series -- B.2 Fourier series for 2?-periodic functions -- List of Symbols -- References En línea: http://dx.doi.org/10.1007/978-0-8176-4448-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35195 Ejemplares
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Título : Approximation Theory XIII: San Antonio 2010 Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Marian Neamtu ; Schumaker, Larry Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Colección: Springer Proceedings in Mathematics, ISSN 2190-5614 num. 13 Número de páginas: XVIII, 418 p Il.: online resource ISBN/ISSN/DL: 978-1-4614-0772-0 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Computer mathematics Approximations and Expansions Computational Numerical Analysis Clasificación: 51 Matemáticas Resumen: These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. The book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related application areas. It contains a carefully refereed and edited selection of papers. Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation. Marian Neamtu is Professor of Mathematics at Vanderbilt University, Nashville, TN. Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University, Nashville, TN Nota de contenido: An Asymptotic Equivalence Between Two Frame Perturbation Theorems - B. A. Bailey -- Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants - H.-P. Blatt, R. Grothmann, and R. K. Kovacheva -- Generalization of Polynomial Interpolation at Chebyshev Nodes - Debao Chen -- Green’s Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines - Gregory E. Fasshauer -- Sparse Recovery Algorithms: Sufficient Conditions in terms of Restricted Isometry Constants - Simon Foucart -- Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function - Michael I. Ganzburg -- Active GeometricWavelets - Itai Gershtansky, Shai Dekel, and Nira Dyn -- Interpolating Composite Systems - Philipp Grohs -- Wavelets and Framelets within the Framework of Nonhomogeneous Wavelet Systems - Bin Han -- Compactly Supported Shearlets - Gitta Kutyniok, Jakob Lemvig, and Wang-Q Lim -- Shearlets on Bounded Domains - Gitta Kutyniok and Wang-Q Lim -- On Christoffel Functions and Related Quantities for Compactly Supported Measures - D. S. Lubinsky -- Exact Solutions of Some Extremal Problems of Approximation Theory - A. L. Lukashov -- A Lagrange Interpolation Method by Trivariate Cubic C1 Splines of Low Locality - G. N¨urnberger and G. Schneider -- Approximation of Besov Vectors by Paley-Wiener Vectors in Hilbert Spaces - Isaac Z. Pesenson and Meyer Z. Pesenson -- A Subclass of the Length Twelve ParameterizedWavelets - David W. Roach -- Geometric Properties of Inverse Polynomial Images - Klaus Schiefermayr -- On Symbolic Computation of Ideal Projectors and Inverse Systems - Boris Shekhtman -- The Dimension of the Space of Smooth Splines of Degree 8 on Tetrahedral Partitions - Xiquan Shi, Ben Kamau, Fengshan Liu, and Baocai Yin -- On Simultaneous Approximation in Function Spaces - Eyad Abu-Sirhan -- Chalmers-Metcalf Operator and Uniqueness of Minimal Projections in ln ¥ and ln1Spaces - Leslaw Skrzypek -- The Polynomial Inverse Image Method - Vilmos Totik -- On Approximation of Periodic Analytic Functions by Linear Combinations of Complex Exponents - Vesselin Vatchev -- Matrix Extension with Symmetry and its Applications - Xiaosheng Zhuang.- En línea: http://dx.doi.org/10.1007/978-1-4614-0772-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32745 Approximation Theory XIII: San Antonio 2010 [documento electrónico] / SpringerLink (Online service) ; Marian Neamtu ; Schumaker, Larry . - New York, NY : Springer New York, 2012 . - XVIII, 418 p : online resource. - (Springer Proceedings in Mathematics, ISSN 2190-5614; 13) .
ISBN : 978-1-4614-0772-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Computer mathematics Approximations and Expansions Computational Numerical Analysis Clasificación: 51 Matemáticas Resumen: These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. The book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related application areas. It contains a carefully refereed and edited selection of papers. Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation. Marian Neamtu is Professor of Mathematics at Vanderbilt University, Nashville, TN. Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University, Nashville, TN Nota de contenido: An Asymptotic Equivalence Between Two Frame Perturbation Theorems - B. A. Bailey -- Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants - H.-P. Blatt, R. Grothmann, and R. K. Kovacheva -- Generalization of Polynomial Interpolation at Chebyshev Nodes - Debao Chen -- Green’s Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines - Gregory E. Fasshauer -- Sparse Recovery Algorithms: Sufficient Conditions in terms of Restricted Isometry Constants - Simon Foucart -- Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function - Michael I. Ganzburg -- Active GeometricWavelets - Itai Gershtansky, Shai Dekel, and Nira Dyn -- Interpolating Composite Systems - Philipp Grohs -- Wavelets and Framelets within the Framework of Nonhomogeneous Wavelet Systems - Bin Han -- Compactly Supported Shearlets - Gitta Kutyniok, Jakob Lemvig, and Wang-Q Lim -- Shearlets on Bounded Domains - Gitta Kutyniok and Wang-Q Lim -- On Christoffel Functions and Related Quantities for Compactly Supported Measures - D. S. Lubinsky -- Exact Solutions of Some Extremal Problems of Approximation Theory - A. L. Lukashov -- A Lagrange Interpolation Method by Trivariate Cubic C1 Splines of Low Locality - G. N¨urnberger and G. Schneider -- Approximation of Besov Vectors by Paley-Wiener Vectors in Hilbert Spaces - Isaac Z. Pesenson and Meyer Z. Pesenson -- A Subclass of the Length Twelve ParameterizedWavelets - David W. Roach -- Geometric Properties of Inverse Polynomial Images - Klaus Schiefermayr -- On Symbolic Computation of Ideal Projectors and Inverse Systems - Boris Shekhtman -- The Dimension of the Space of Smooth Splines of Degree 8 on Tetrahedral Partitions - Xiquan Shi, Ben Kamau, Fengshan Liu, and Baocai Yin -- On Simultaneous Approximation in Function Spaces - Eyad Abu-Sirhan -- Chalmers-Metcalf Operator and Uniqueness of Minimal Projections in ln ¥ and ln1Spaces - Leslaw Skrzypek -- The Polynomial Inverse Image Method - Vilmos Totik -- On Approximation of Periodic Analytic Functions by Linear Combinations of Complex Exponents - Vesselin Vatchev -- Matrix Extension with Symmetry and its Applications - Xiaosheng Zhuang.- En línea: http://dx.doi.org/10.1007/978-1-4614-0772-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32745 Ejemplares
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