Theses (Scuola Normale Superiore)

Structured Matrix Based Methods for Approximate Polynomial GCD

Authors: Boito, Paola

  • 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

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)

Buy this book

eBook $14.99
price for USA (gross)
  • ISBN 978-88-7642-381-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $24.95
price for USA
  • ISBN 978-88-7642-380-2
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Structured Matrix Based Methods for Approximate Polynomial GCD
Authors
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
Edition Number
1
Number of Pages
250
Topics