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Hybrid Krylov methods for nonlinear systems of equations. (English) Zbl 0708.65049
Several hybrid methods combining Newton-like methods with Krylov methods are considered. In particular, the solving of approximations of the linear equations of Newton’s method via Arnoldi’s method and the generalized minimum residual method (GMRES) is studied. For large systems these methods have the advantage that essentially only matrix products need to be computed and stored. To globalize the nonlinear methods the authors incorporate and study a linesearch backtracking method and a trust region technique based upon Powell’s hybrid method with a dogleg strategy. Numerical implementations are tested on a Bratú type problem and a driven cavity problem.

65H10 Numerical computation of solutions to systems of equations
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