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Structured Matrix Based Methods for Approximate Polynomial GCD: 15 2011th Edition
Author(s): Paola Boito (Author)
- Publisher: Scuola Normale Superiore
- Publication Date: 12 July 2011
- Edition: 2011th
- Language: English
- Print length: 250 pages
- ISBN-10: 9788876423802
- ISBN-13: 9788876423802
Book Description
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation.
Editorial Reviews
From the Back Cover
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.
