CG Type Algorithm for Indefinite Linear Systems 1 Conjugate Gradient Type Methods for Solving Symmetric , Inde nite
نویسنده
چکیده
The conjugate gradient algorithm (CG) is an eeective tool for solving a system of linear equation with a positive deenite coeecient matrix. We show the reasons for a possible breakdown of the method when applied to a symmetric system with an indeenite coeecient matrix. Although in nite arithmetic a breakdown of the method occurs rather seldom, near breakdowns may slow down the speed of convergence. We propose a look-ahead technique to overcome these near breakdowns. Moreover, we present a modiication of the CG algorithm applicable to symmetric indeenite systems (CGI). The CGI algorithm is nearly as eecient as the plain CG algorithm. We compared the CGI algorithm with a modiication of the composite step bi-conjugate gradient algorithm of Bank and Chan.
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