Look-ahead in Bi-CGSTAB and other product methods for linear systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Look-ahead in Bi-CGSTAB and other product methods for linear systems

Authors:	C. Brezinski M. Redivo-Zaglia

Affiliation:	(1) Laboratoire d'Analyse Numérique et d'Optimisation, UFR IEEA - M3, Université des Sciences et Technologies de Lille, Villeneuve d'Ascq, F-59655 Cedex, France;(2) Dipartimento di Elettronica e Informatica, Università degli Studi di Padova, via Gradenigo 6/a, I-35131 Padova, Italy

Abstract:	The Lanczos method for solvingAx = b consists in constructing the sequence of vectorsx_k such thatr_k =b – Ax_k =P_k(A)r₀ whereP_k is the orthogonal polynomial of degree at mostk with respect to the linear functionalc whose moments arec(_i) =c_i = (y, Aⁱr₀).In this paper we discuss how to avoid breakdown and near-breakdown in a whole class of methods defined byr_k =Q_k(A)P_k(A)r₀,Q_k being a given polynomial. In particular, the case of the Bi-CGSTAB algorithm is treated in detail. Some other choices of the polynomialsQ_k are also studied.

Keywords:	Linear equations iterative methods
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