论文信息 - On Grau's method for simultaneous factorization of polynomials

On Grau's method for simultaneous factorization of polynomials

This note is concerned with A. A. Grau’s method [SIAM J. Numer. Anal., 8 (1971), pp. 425–438.] for simultaneous factorization of polynomials as a generalisation of the famous Durand–Kerner method. Grau’s method is discussed on a general level such that certain invariance properties are obtained. This yields a matrix interpretation that facilitates error estimates by Gershgorin’s theorem. A convergence result is proved that increases the usual quadratic convergence. Finally a single-step version is stated, which has R-order of convergence greater than 2.

Carsten Carstensen | C. Carstensen

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