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.

Structured Matrix Based Methods for Approximate Polynomial GCD

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Paperback / softback by Paola Boito

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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.... Read more

    Publisher: Birkhauser Verlag AG
    Publication Date: 12/07/2011
    ISBN13: 9788876423802, 978-8876423802
    ISBN10: 887642380X

    Number of Pages: 250

    Non Fiction , Mathematics & Science , Education

    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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