CG Versus MINRES: An Empirical Comparison

By David Chin-Lung Fong, Michael A. Saunders. 2012

84 citations recorded by the source corpus.

For iterative solution of symmetric systems  the conjugate gradient method (CG) is commonly used when A is positive definite, while the minimum residual method (MINRES) is typically reserved for indefinite systems. We investigate the sequence of approximate solutions  generated by each method and suggest that even if A is positive definite, MINRES may be preferable to CG if iterations are to be terminated early. In particular, we show for MINRES that the solution norms  are monotonically increasing when A is positive definite (as was already known for CG), and the solution errors  are monotonically decreasing. We also show that the backward errors for the MINRES iterates  are monotonically decreasing.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/77f13b22311118b4c0e75c518c02f9fee0b8bbb3