Titlebook: Structured Matrix Based Methods for Approximate Polynomial GCD; Paola Boito Book 2011 The Editor(s) (if applicable) and The Author(s), und

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A fast GCD algorithm,The algorithms for approximate GCD computation outlined in the previous chapters all have a computational cost which is cubic in the degrees of the polynomials. The only exception is the Euclidean algorithm, which however, in addition to troublesome stability issues, might fail to return an approximate divisor of maximum degree.

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Numerical tests,The algorithms presented in Chapters 6 and 7 have been implemented in Matlab and applied to a wide variety of test polynomials, chosen as to be representative of the main difficulties that are typical of approximate GCD algorithms.

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Generalizations and further work,The present work focuses on properties and computation of an approximate GCD of two univariate polynomials, which are expressed through their coefficients in the usual monomial basis.

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Paola BoitoTopics situated at the crossroads between two fields of increasing interest to the mathematical community: symbolic-numeric polynomial computation and structured numerical linear algebra.Survey of the

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Structured and resultant matrices,mon root if and only if the determinant of this matrix (which is often called the .) is zero. Moreover, the degree of the GCD of the two polynomials is equal to the rank deficiency of the resultant matrix.

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