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Shao-Liang Zhang

2011-09-16
14:20:00 - 15:10:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

There is a strong need for the fast solution of nonsymmetric linear systems Ax=b which arise frequently in the field of scientific computing as subproblems or as intermediate steps. For solving large nonsymmetric linear systems, direct methods, such as LU factorization, are often prohibitive both in terms of computation time and memory storage. For this reason, the research on Krylov-subspace methods as an alternative has been the dominant paradigm in the field of numerical algebra since the publication of a paper by Lanczos in the 1950s. In his paper, Lanczos proposed the Bi-Conjugate Gradient method (Bi-CG hereafter) which was revived by Fletcher for solving nonsymmetric linear systems. The aim of this talk is to highlight two kinds of attempts to improve the convergence behaviour of Bi-CG in past 2 decades.

This is a joint work with Tomohiro Sogabe.