Structured Matrix Based Methods for Approximate Polynomial GCD

You must be logged in to access this title.

Sign up now

Already a member? Log in

Synopsis

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.

Book details

Edition:
2011
Series:
Publications of the Scuola Normale Superiore (Book 15)
Author:
Paola Boito
ISBN:
9788876423819
Related ISBNs:
9788876423802
Publisher:
Scuola Normale Superiore
Pages:
250
Reading age:
Not specified
Includes images:
No
Date of addition:
2022-06-20
Usage restrictions:
Copyright
Copyright date:
2011
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction