Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration

摘要: An important variation of preconditioned conjugate gradient algorithms is inexact preconditioner implemented with inner-outer iterations [G. H. Golub and M. L. Overton, Numerical Analysis, Lecture Notes in Math. 912, Springer, Berlin, New York, 1982], where the solved by an inner iteration to a prescribed precision. In this paper, we formulate algorithm for symmetric positive definite system analyze its convergence property. We establish linear result using local relation residual norms. also global equation show that may have superlinear property when high accuracy. The analysis agreement observed numerical behavior algorithm. particular, it suggests heuristic choice stopping threshold iteration. examples are given effectiveness compare bound.