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Structured Matrix Based Methods for Approximate Polynomial GCD

Name: Structured Matrix Based Methods for Approximate Polynomial GCD
Brand: Birkhauser Verlag AG
SKU: 01967796
Price: 27.44 EUR
Availability: InStock
Author: Paola Boito
ISBN: 9788876423802

Paola Boito

Language

English

Book Paperback

Libristo code: 01967796

Publishers Birkhauser Verlag AG, July 2011

Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a c... Full description

Libristo code: 01967796

66 b

27.44 €

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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.