Structured Matrix Based Methods for Approximate Polynomial GCD
Authors: Boito, Paola
Free Preview- Topics situated at the crossroads between two fields of increasing interest to the mathematical community: symbolic-numeric polynomial computation and structured numerical linear algebra
- Survey of the main tools and techniques used in either domain
- State-of-the-art methods that exploit matrix structure to improve the performance of polynomial computations
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- About this book
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Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.
- Table of contents (9 chapters)
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Approximate polynomial GCD
Pages 1-20
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Structured and resultant matrices
Pages 21-43
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The Euclidean algorithm
Pages 45-58
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Matrix factorization and approximate GCDs
Pages 59-70
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Optimization approach
Pages 71-82
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Structured Matrix Based Methods for Approximate Polynomial GCD
- Authors
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- Paola Boito
- Series Title
- Theses (Scuola Normale Superiore)
- Series Volume
- 15
- Copyright
- 2011
- Publisher
- Edizioni della Normale
- Copyright Holder
- Scuola Normale Superiore Pisa
- eBook ISBN
- 978-88-7642-381-9
- DOI
- 10.1007/978-88-7642-381-9
- Softcover ISBN
- 978-88-7642-380-2
- Series ISSN
- 2239-1460
- Edition Number
- 1
- Number of Pages
- 250
- Topics
