A.J. Hughes Hallett: Second-order iterations with guaranteed convergence

A.J. Hughes Hallett: Second-order iterations with guaranteed convergence

Recent results on optimal extrapolations of first-order stationary iterations have shown that they are necessarily divergent in a wide class of problems. This paper examines a second-order iterative process which is guaranteed to converge — in particular when applied to the solution of an arbitrary equation system. A general convergence theory for semi-iterative techniques is established at the same time.

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