Nonlinear orthomin(k) methods

摘要

Nonlinear orthomin(1) for solving nonlinear systems of equations as presented and analyzed by A.T. Chronopoulos [J. Comput. Appl. Math. 40 (1992) 7389]. His method is a nonlinear generalization of orthomin(1) in linear cases. In this paper, orthomin(k) for linear systems is generalized to nonlinear orthomin(k) which can be applied directly to nonlinear operator equations. Under the same conditions as nonlinear orthomin(1) the nonlinear orthomin(k) method was proved to converge to a globally unique solution.