Analysis of peaks and plateaus in a Galerkin/minimal residual pair of methods for solving Ax=b

Irregular peaks often appear if we use Galerkin methods for solving linear systems of equations Ax=b. These peaks bring about too difficult to identify convergence. To remedy this disadvantage, we have to spend more work and memory, that is we use norm minimizing methods for solving Ax=b. However, plateaus cannot be avoided. In this paper we give a sufficient and necessary condition for occurring of peaks. Also we present some related factors for this behavior.

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