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Conjugate gradient and minimal residual methods for solving symmetric indefinite systems

✍ Scribed by Yu-Ling Lai; Wen-Wei Lin; Dan'l Pierce

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
941 KB
Volume
84
Category
Article
ISSN
0377-0427

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✦ Synopsis

Norm-minimizing-type methods for solving large sparse linear systems with symmetric and indefinite coefficient matrices are considered. The Krylov subspace can be generated by either the Lanczos approach, such as the methods MINRES, GMRES and QMR, or by a conjugate-gradient approach. Here, we propose an algorithm based on the latter approach. Some relations among the search directions and the residuals, and how the search directions are related to the Krylov subspace are investigated. Numerical experiments are reported to verify the convergence properties.

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