Hard Cases for Conjugate Gradient Method
نویسندگان
چکیده
The Conjugate Gradient (CG) method is often used to solve a positive definite linear system Ax = b. This paper analyzes two hard cases for CG or any Krylov subspace type methods by either analytically finding the residual formulas or tightly bound the residuals from above and below, in contrast to existing results which only bound residuals from above. The analysis is based on a general framework to estimate CG and GMRES residuals for certain linear systems with normal A, and the framework may potentially be useful elsewhere.
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