Structured Matrices and Polynomials: Unified Superfast Algorithms
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2001
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study |
| Beschreibung: | 1 Online-Ressource (XXV, 278 p) |
| ISBN: | 9781461201298 9781461266259 |
| DOI: | 10.1007/978-1-4612-0129-8 |
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| 500 | |a Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study | ||
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Datensatz im Suchindex
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| author | Pan, Victor Y. |
| author_facet | Pan, Victor Y. |
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| author_sort | Pan, Victor Y. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-0129-8 |
| format | Electronic eBook |
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| isbn | 9781461201298 9781461266259 |
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| spelling | Pan, Victor Y. Verfasser aut Structured Matrices and Polynomials Unified Superfast Algorithms by Victor Y. Pan Boston, MA Birkhäuser Boston 2001 1 Online-Ressource (XXV, 278 p) txt rdacontent c rdamedia cr rdacarrier Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study Mathematics Information theory Computer science Matrix theory Computer science / Mathematics Linear and Multilinear Algebras, Matrix Theory Theory of Computation Mathematics of Computing Computational Mathematics and Numerical Analysis Informatik Mathematik Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Polynom (DE-588)4046711-9 s Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Matrix Mathematik (DE-588)4037968-1 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-0129-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pan, Victor Y. Structured Matrices and Polynomials Unified Superfast Algorithms Mathematics Information theory Computer science Matrix theory Computer science / Mathematics Linear and Multilinear Algebras, Matrix Theory Theory of Computation Mathematics of Computing Computational Mathematics and Numerical Analysis Informatik Mathematik Datenverarbeitung (DE-588)4011152-0 gnd Polynom (DE-588)4046711-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4046711-9 (DE-588)4037968-1 |
| title | Structured Matrices and Polynomials Unified Superfast Algorithms |
| title_auth | Structured Matrices and Polynomials Unified Superfast Algorithms |
| title_exact_search | Structured Matrices and Polynomials Unified Superfast Algorithms |
| title_full | Structured Matrices and Polynomials Unified Superfast Algorithms by Victor Y. Pan |
| title_fullStr | Structured Matrices and Polynomials Unified Superfast Algorithms by Victor Y. Pan |
| title_full_unstemmed | Structured Matrices and Polynomials Unified Superfast Algorithms by Victor Y. Pan |
| title_short | Structured Matrices and Polynomials |
| title_sort | structured matrices and polynomials unified superfast algorithms |
| title_sub | Unified Superfast Algorithms |
| topic | Mathematics Information theory Computer science Matrix theory Computer science / Mathematics Linear and Multilinear Algebras, Matrix Theory Theory of Computation Mathematics of Computing Computational Mathematics and Numerical Analysis Informatik Mathematik Datenverarbeitung (DE-588)4011152-0 gnd Polynom (DE-588)4046711-9 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Mathematics Information theory Computer science Matrix theory Computer science / Mathematics Linear and Multilinear Algebras, Matrix Theory Theory of Computation Mathematics of Computing Computational Mathematics and Numerical Analysis Informatik Mathematik Datenverarbeitung Polynom Matrix Mathematik |
| url | https://doi.org/10.1007/978-1-4612-0129-8 |
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