Brown, Peter N.; Saad, Youcef Hybrid Krylov methods for nonlinear systems of equations. (English) Zbl 0708.65049 SIAM J. Sci. Stat. Comput. 11, No. 3, 450-481 (1990). 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. Reviewer: Eugene L. Allgower (Fort Collins) Cited in 2 ReviewsCited in 205 Documents MSC: 65H10 Numerical computation of solutions to systems of equations Keywords:inexact Newton methods; conjugate gradient methods; Krylov methods; Arnoldi’s method; generalized minimum residual method; nonlinear methods; linesearch backtracking method; trust region technique; Powell’s hybrid method; Bratú type problem; driven cavity problem PDFBibTeX XMLCite \textit{P. N. Brown} and \textit{Y. Saad}, SIAM J. Sci. Stat. Comput. 11, No. 3, 450--481 (1990; Zbl 0708.65049) Full Text: DOI