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Dynamic acceleration of nonlinear iterations. (English) Zbl 0594.65033

Elliptic problem solvers II, Proc. Conf., Monterey/Calif. 1983, 301-313 (1984).
[For the entire collection see Zbl 0557.00009.]
The situation is considered where a production code uses a suboptimal iterative method to solve systems of nonlinear equations. Then there is interest in accelerating the convergence with a minimal impact on the original code. It is assumed that the original code produces iterates \(\{v_ i\}\) that can be well approximated by a linear recurrence \(v_{i+1}=G_ iv_ i+b_ i\) where \(G_ i\) and \(b_ i\) vary slowly, but that Jacobian matrices are not available. On the basis of this model, eigenvalue estimates are obtained at each step which in turn are used to find parameters for one-step and two-step acceleration schemes. The viability of the linear model is monitored at each step and the implication of trust region strategies on the choice of parameters is considered. Some numerical results illustrate the effectiveness of the acceleration techniques.
Reviewer: W.C.Rheinboldt

MSC:

65H10 Numerical computation of solutions to systems of equations

Citations:

Zbl 0557.00009