TR-2002003: Univariate Polynomial Root-Finding with a Lower Computational Precision and Higher Convergence Rates
نویسنده
چکیده
Univariate polynoimial rootnding is an oldest classical problem, which is still an important research topic, due to its impact on computational algebra and geometry. The Weierstrass (Durand{Kerner) approach and its variations are most popular practical choices for simultaneous approximation of all roots of a polynomial, but these methods require computations with a high multiple precision. We apply some novel techniques of structured matrix computations to avoid this serious de ciency, thus giving decisive acceleration to the approach. We also show two ways (based on the Lagrange interpolation formula and on Newton's iteration for the eigenproblem for a generalized companion matrix) to unifying the derivation of the Weierstrass (Durand{ Kerner) algorithm (having quadratic convergence) and its extensions having convergence rates 4; 6; 8; : : : , and we study application of the inverse power iteration to (generalized) companion matrix for polynomial rootnding. Supported by NSF Grant CCR 9732206 and PSC CUNY Award 66383-0032
منابع مشابه
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