Abstract
Consideration of an abstract improvement algorithm leads to the following principle, which is similar to that underlying iterative refinement: By making judicious use of relatively few high accuracy computations, high accuracy solutions can be obtained very efficiently by the algorithm. This principle is applied specifically to ${\text{GMRES}}(m)$ here; it can be similarly applied to a number of other “restarted” iterative linear methods as well. Results are given for numerical experiments in solving a discretized linear elliptic boundary value problem and in computing a step of an inexact Newton method using finite differences for a discretized nonlinear elliptic boundary value problem.
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More From: SIAM Journal on Scientific and Statistical Computing
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