ENGLISH

Structured Matrix Based Methods for Approximate Polynomial GCD

By Paola Boito (auth.)

Book information

Publisher
Edizioni della Normale
Year
2011
ISBN
978-88-7642-380-2, 978-88-7642-381-9
DOI
10.1007/978-88-7642-381-9
Language
english
Format
PDF
Filesize
1 MB (1208865 bytes)
Series
Tesi/Theses 15
Edition
1
Pages
250\207
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Algebra

Description

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.

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