Resultado de la búsqueda
72 búsqueda de la palabra clave 'Matrix'
Refinar búsqueda Generar rss de la búsqueda
Link de la búsqueda
Título : Matrix-Based Multigrid : Theory and Applications Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Shapira, Yair Editorial: Boston, MA : Springer US Fecha de publicación: 2008 Colección: Numerical Methods and Algorithms, ISSN 1571-5698 num. 2 Número de páginas: XXIV, 318 p Il.: online resource ISBN/ISSN/DL: 978-0-387-49765-5 Idioma : Inglés (eng) Palabras clave: Mathematics Numerical analysis Matrix theory Algebra Mathematical Analysis (Mathematics) Computer mathematics Computational intelligence and Numeric Computing Linear Multilinear Algebras, Theory Intelligence Clasificación: 51 Matemáticas Resumen: Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains. Key Features of this Second Edition: - Discusses multigrid methods from the domain decomposition viewpoint, thus making the material accessible to beginning undergraduate/graduate students - Uses the semialgebraic multigrid approach to handle complex topics (such as the solution of systems of PDEs) - Provides relevant and insightful exercises at the end of each chapter which help reinforce the material - Uses numerous illustrations and examples to motivate the subject matter - Covers important applications in physics, engineering and computer science Matrix-Based Multigrid can serve as a textbook for courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered, the only prerequisites are elementary linear algebra and calculus. Excerpts from the reviews of the first edition: "This book contains a wealth of information about using multilevel methods to solve partial differential equations (PDEs). . . A common matrix-based framework for developing these methods is used throughout the book. This approach allows methods to be developed for problems under three very different conditions. . . This book will be insightful for practitioners in the field. . . students will enjoy studying this book to see how the many puzzle pieces of the multigrid landscape fit together." (Loyce Adams, SIAM review, Vol. 47(3), 2005) "The discussion very often includes important applications in physics, engineering, and computer science. The style is clear, the details can be understood without any serious prerequisite. The usage of multigrid method for unstructured grids is exhibited by a well commented C++ program. This way the book is suitable for anyone . . . who needs numerical solution of partial differential equations." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004) Nota de contenido: Concepts and Preliminaries -- The Multilevel-Multiscale Approach -- Preliminaries -- Partial Differential Equations and Their Discretization -- Finite Differences and Volumes -- Finite Elements -- The Numerical Solution of Large Sparse Linear Systems of Algebraic Equations -- Iterative Linear System Solvers -- The Multigrid Iteration -- Matrix-Based Multigrid for Structured Grids -- The Automatic Multigrid Method -- Applications in Image Processing -- The Black-Box Multigrid Method -- The Indefinite Helmholtz Equation -- Matrix-Based Semicoarsening Method -- Matrix-Based Multigrid for Semistructured Grids -- Matrix-Based Multigrid for Locally Refined Meshes -- Application to Semistructured Grids -- Matrix-Based Multigrid for Unstructured Grids -- The Domain-Decomposition Multigrid Method -- The Algebraic Multilevel Method -- Applications -- Semialgebraic Multilevel Method for Systems of Partial Differential Equations -- Appendices -- Time-Dependent Parabolic PDEs -- Nonlinear Equations En línea: http://dx.doi.org/10.1007/978-0-387-49765-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34149 Matrix-Based Multigrid : Theory and Applications [documento electrónico] / SpringerLink (Online service) ; Shapira, Yair . - Boston, MA : Springer US, 2008 . - XXIV, 318 p : online resource. - (Numerical Methods and Algorithms, ISSN 1571-5698; 2) .
ISBN : 978-0-387-49765-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Numerical analysis Matrix theory Algebra Mathematical Analysis (Mathematics) Computer mathematics Computational intelligence and Numeric Computing Linear Multilinear Algebras, Theory Intelligence Clasificación: 51 Matemáticas Resumen: Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and domains. Key Features of this Second Edition: - Discusses multigrid methods from the domain decomposition viewpoint, thus making the material accessible to beginning undergraduate/graduate students - Uses the semialgebraic multigrid approach to handle complex topics (such as the solution of systems of PDEs) - Provides relevant and insightful exercises at the end of each chapter which help reinforce the material - Uses numerous illustrations and examples to motivate the subject matter - Covers important applications in physics, engineering and computer science Matrix-Based Multigrid can serve as a textbook for courses in numerical linear algebra, numerical methods for PDEs, and computational physics at the advanced undergraduate and graduate levels. Since most of the background material is covered, the only prerequisites are elementary linear algebra and calculus. Excerpts from the reviews of the first edition: "This book contains a wealth of information about using multilevel methods to solve partial differential equations (PDEs). . . A common matrix-based framework for developing these methods is used throughout the book. This approach allows methods to be developed for problems under three very different conditions. . . This book will be insightful for practitioners in the field. . . students will enjoy studying this book to see how the many puzzle pieces of the multigrid landscape fit together." (Loyce Adams, SIAM review, Vol. 47(3), 2005) "The discussion very often includes important applications in physics, engineering, and computer science. The style is clear, the details can be understood without any serious prerequisite. The usage of multigrid method for unstructured grids is exhibited by a well commented C++ program. This way the book is suitable for anyone . . . who needs numerical solution of partial differential equations." (Peter Hajnal, Acta Scientiarum Mathematicarum, Vol. 70, 2004) Nota de contenido: Concepts and Preliminaries -- The Multilevel-Multiscale Approach -- Preliminaries -- Partial Differential Equations and Their Discretization -- Finite Differences and Volumes -- Finite Elements -- The Numerical Solution of Large Sparse Linear Systems of Algebraic Equations -- Iterative Linear System Solvers -- The Multigrid Iteration -- Matrix-Based Multigrid for Structured Grids -- The Automatic Multigrid Method -- Applications in Image Processing -- The Black-Box Multigrid Method -- The Indefinite Helmholtz Equation -- Matrix-Based Semicoarsening Method -- Matrix-Based Multigrid for Semistructured Grids -- Matrix-Based Multigrid for Locally Refined Meshes -- Application to Semistructured Grids -- Matrix-Based Multigrid for Unstructured Grids -- The Domain-Decomposition Multigrid Method -- The Algebraic Multilevel Method -- Applications -- Semialgebraic Multilevel Method for Systems of Partial Differential Equations -- Appendices -- Time-Dependent Parabolic PDEs -- Nonlinear Equations En línea: http://dx.doi.org/10.1007/978-0-387-49765-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34149 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Matrix Theory : Basic Results and Techniques Tipo de documento: documento electrónico Autores: Fuzhen Zhang ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVII, 399 p. 8 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-1099-7 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Operator Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -The inclusion of more than 1000 exercises -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. Prerequisites include a decent background in elementary linear algebra and calculus. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Fuzhen Zhang is a professor of mathematics at Nova Southeastern University, Fort Lauderdale, Florida. He received his Ph.D. in Mathematics from the University of California at Santa Barbara, M.S. from Beijing Normal University, and B.Sc. from Shenyang Normal University (China). In addition to research papers, he is the author of the book Linear Algebra: Challenging Problems for Students and the editor of The Schur Complement and Its Applications Nota de contenido: Preface to the Second Edition -- Preface -- Frequently Used Notation and Terminology -- Frequently Used Terms -- 1 Elementary Linear Algebra Review -- 2 Partitioned Matrices, Rank, and Eigenvalues -- 3 Matrix Polynomials and Canonical Forms -- 4 Numerical Ranges, Matrix Norms, and Special Operations -- 5 Special Types of Matrices -- 6 Unitary Matrices and Contractions -- 7 Positive Semidefinite Matrices -- 8 Hermitian Matrices -- 9 Normal Matrices -- 10 Majorization and Matrix Inequalities -- References -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1099-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33233 Matrix Theory : Basic Results and Techniques [documento electrónico] / Fuzhen Zhang ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVII, 399 p. 8 illus., 1 illus. in color : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4614-1099-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Operator Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: The aim of this book is to concisely present fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. The book contains ten chapters covering various topics ranging from similarity and special types of matrices to Schur complements and matrix normality. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. Major changes in this revised and expanded second edition: -Expansion of topics such as matrix functions, nonnegative matrices, and (unitarily invariant) matrix norms -The inclusion of more than 1000 exercises -A new chapter, Chapter 4, with updated material on numerical ranges and radii, matrix norms, and special operations such as the Kronecker and Hadamard products and compound matrices -A new chapter, Chapter 10, on matrix inequalities, which presents a variety of inequalities on the eigenvalues and singular values of matrices and unitarily invariant norms. This book can be used as a textbook or a supplement for a linear algebra and matrix theory class or a seminar for senior undergraduate or graduate students. Prerequisites include a decent background in elementary linear algebra and calculus. The book can also serve as a reference for instructors and researchers in the fields of algebra, matrix analysis, operator theory, statistics, computer science, engineering, operations research, economics, and other fields. Fuzhen Zhang is a professor of mathematics at Nova Southeastern University, Fort Lauderdale, Florida. He received his Ph.D. in Mathematics from the University of California at Santa Barbara, M.S. from Beijing Normal University, and B.Sc. from Shenyang Normal University (China). In addition to research papers, he is the author of the book Linear Algebra: Challenging Problems for Students and the editor of The Schur Complement and Its Applications Nota de contenido: Preface to the Second Edition -- Preface -- Frequently Used Notation and Terminology -- Frequently Used Terms -- 1 Elementary Linear Algebra Review -- 2 Partitioned Matrices, Rank, and Eigenvalues -- 3 Matrix Polynomials and Canonical Forms -- 4 Numerical Ranges, Matrix Norms, and Special Operations -- 5 Special Types of Matrices -- 6 Unitary Matrices and Contractions -- 7 Positive Semidefinite Matrices -- 8 Hermitian Matrices -- 9 Normal Matrices -- 10 Majorization and Matrix Inequalities -- References -- Notation -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1099-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33233 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Applied Linear Algebra and Matrix Analysis Tipo de documento: documento electrónico Autores: Shores, Thomas S ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Undergraduate Texts in Mathematics, ISSN 0172-6056 Número de páginas: XII, 384 p. 27 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-48947-6 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics *Gaussian elimination and other operations with matrices *basic properties of matrix and determinant algebra *standard Euclidean spaces, both real and complex *geometrical aspects of vectors, such as norm, dot product, and angle *eigenvalues, eigenvectors, and discrete dynamical systems *general norm and inner-product concepts for abstract vector spaces For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory Nota de contenido: Linear Systems Of Equations -- Matrix Algebra -- Vector Spaces -- Geometrical Aspects Of Standard Spaces -- The Eigenvalue Problem -- Geometrical Aspects Of Abstract Spaces En línea: http://dx.doi.org/10.1007/978-0-387-48947-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34485 Applied Linear Algebra and Matrix Analysis [documento electrónico] / Shores, Thomas S ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XII, 384 p. 27 illus : online resource. - (Undergraduate Texts in Mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-48947-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Linear and Multilinear Algebras, Theory Clasificación: 51 Matemáticas Resumen: This new book offers a fresh approach to matrix and linear algebra by providing a balanced blend of applications, theory, and computation, while highlighting their interdependence. Intended for a one-semester course, Applied Linear Algebra and Matrix Analysis places special emphasis on linear algebra as an experimental science, with numerous examples, computer exercises, and projects. While the flavor is heavily computational and experimental, the text is independent of specific hardware or software platforms. Throughout the book, significant motivating examples are woven into the text, and each section ends with a set of exercises. The student will develop a solid foundation in the following topics *Gaussian elimination and other operations with matrices *basic properties of matrix and determinant algebra *standard Euclidean spaces, both real and complex *geometrical aspects of vectors, such as norm, dot product, and angle *eigenvalues, eigenvectors, and discrete dynamical systems *general norm and inner-product concepts for abstract vector spaces For many students, the tools of matrix and linear algebra will be as fundamental in their professional work as the tools of calculus; thus it is important to ensure that students appreciate the utility and beauty of these subjects as well as the mechanics. By including applied mathematics and mathematical modeling, this new textbook will teach students how concepts of matrix and linear algebra make concrete problems workable. Thomas S. Shores is Professor of Mathematics at the University of Nebraska, Lincoln, where he has received awards for his teaching. His research touches on group theory, commutative algebra, mathematical modeling, numerical analysis, and inverse theory Nota de contenido: Linear Systems Of Equations -- Matrix Algebra -- Vector Spaces -- Geometrical Aspects Of Standard Spaces -- The Eigenvalue Problem -- Geometrical Aspects Of Abstract Spaces En línea: http://dx.doi.org/10.1007/978-0-387-48947-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34485 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Combinatorial Matrix Theory and Generalized Inverses of Matrices / SpringerLink (Online service) ; Ravindra B. Bapat ; Steve J. Kirkland ; K. Manjunatha Prasad ; Simo Puntanen (2013)
Título : Combinatorial Matrix Theory and Generalized Inverses of Matrices Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Ravindra B. Bapat ; Steve J. Kirkland ; K. Manjunatha Prasad ; Simo Puntanen Editorial: India : Springer India Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XVII, 277 p. 53 illus., 36 illus. in color Il.: online resource ISBN/ISSN/DL: 978-81-322-1053-5 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Statistics Linear and Multilinear Algebras, Theory Statistical Methods Clasificación: 51 Matemáticas Resumen: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India Nota de contenido: Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube -- Notes on Explicit Block Diagonalization -- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs -- Matrix Product of Graphs -- Determinant of the Laplacian Matrix of Weighted Directed Graphs -- From Multivariate Skewed Distributions to Copulas -- Revisiting the BLUE in a Linear Model via Proper Eigenvectors -- Inference in Error Orthogonal Models -- On the Entries of Orthogonal Projection Matrices -- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces -- The Reverse Order Law in Indefinite Inner Product Spaces -- Generalized Inverses and Approximation Numbers -- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space -- Products and Sums of Idempotent Matrices over Principal Ideal Domain -- Perfect Semiring of Nonnegative Matrices -- Regular Matrices over an Incline -- Matrix Partial Orders associated with Space Preorder -- An Illustrated Introduction to Some Old Magic Squares from India -- Appendix: Report on CMTGIM 2012, Manipal -- Index En línea: http://dx.doi.org/10.1007/978-81-322-1053-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32623 Combinatorial Matrix Theory and Generalized Inverses of Matrices [documento electrónico] / SpringerLink (Online service) ; Ravindra B. Bapat ; Steve J. Kirkland ; K. Manjunatha Prasad ; Simo Puntanen . - India : Springer India : Imprint: Springer, 2013 . - XVII, 277 p. 53 illus., 36 illus. in color : online resource.
ISBN : 978-81-322-1053-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Statistics Linear and Multilinear Algebras, Theory Statistical Methods Clasificación: 51 Matemáticas Resumen: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India Nota de contenido: Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube -- Notes on Explicit Block Diagonalization -- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs -- Matrix Product of Graphs -- Determinant of the Laplacian Matrix of Weighted Directed Graphs -- From Multivariate Skewed Distributions to Copulas -- Revisiting the BLUE in a Linear Model via Proper Eigenvectors -- Inference in Error Orthogonal Models -- On the Entries of Orthogonal Projection Matrices -- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces -- The Reverse Order Law in Indefinite Inner Product Spaces -- Generalized Inverses and Approximation Numbers -- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space -- Products and Sums of Idempotent Matrices over Principal Ideal Domain -- Perfect Semiring of Nonnegative Matrices -- Regular Matrices over an Incline -- Matrix Partial Orders associated with Space Preorder -- An Illustrated Introduction to Some Old Magic Squares from India -- Appendix: Report on CMTGIM 2012, Manipal -- Index En línea: http://dx.doi.org/10.1007/978-81-322-1053-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32623 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar
Título : Factorization of Matrix and Operator Functions: The State Space Method Tipo de documento: documento electrónico Autores: Harm Bart ; SpringerLink (Online service) ; André C. M. Ran ; Israel Gohberg ; Marinus A. Kaashoek Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Operator Theory: Advances and Applications, Linear Operators and Linear Systems num. 178 Número de páginas: XII, 412 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8268-1 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Operator Number Theory Linear and Multilinear Algebras, Clasificación: 51 Matemáticas Resumen: The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces Nota de contenido: Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions En línea: http://dx.doi.org/10.1007/978-3-7643-8268-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34386 Factorization of Matrix and Operator Functions: The State Space Method [documento electrónico] / Harm Bart ; SpringerLink (Online service) ; André C. M. Ran ; Israel Gohberg ; Marinus A. Kaashoek . - Basel : Birkhäuser Basel, 2008 . - XII, 412 p : online resource. - (Operator Theory: Advances and Applications, Linear Operators and Linear Systems; 178) .
ISBN : 978-3-7643-8268-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Operator Number Theory Linear and Multilinear Algebras, Clasificación: 51 Matemáticas Resumen: The present book deals with factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, theory of job scheduling in operations research. The book systematically employs a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. This principle allows one to deal with different factorizations from one point of view. Covered are canonical factorization, minimal and non-minimal factorizations, pseudo-canonical factorization, and various types of degree one factorization. Considerable attention is given to the matter of stability of factorization which in terms of the state space method involves stability of invariant subspaces.invariant subspaces Nota de contenido: Motivating Problems, Systems and Realizations -- Motivating Problems -- Operator Nodes, Systems, and Operations on Systems -- Various Classes of Systems -- Realization and Linearization of Operator Functions -- Factorization and Riccati Equations -- Canonical Factorization and Applications -- Minimal Realization and Minimal Factorization -- Minimal Systems -- Minimal Realizations and Pole-Zero Structure -- Minimal Factorization of Rational Matrix Functions -- Degree One Factors, Companion Based Rational Matrix Functions, and Job Scheduling -- Factorization into Degree One Factors -- Complete Factorization of Companion Based Matrix Functions -- Quasicomplete Factorization and Job Scheduling -- Stability of Factorization and of Invariant Subspaces -- Stability of Spectral Divisors -- Stability of Divisors -- Factorization of Real Matrix Functions En línea: http://dx.doi.org/10.1007/978-3-7643-8268-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34386 Ejemplares
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Permalink
PermalinkPermalinkPermalinkPermalink
