CONVERGENCE THEORY OF NONLINEAR NEWTON-KRYLOV ALGORITHMS

This paper presents some convergence theory for nonlinear Krylov subsp ace methods. The basic idea of these methods, which have been describe d by the authors in an earlier paper, is to use variants of Newton's i teration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspac e of small dimension. The main focus of this paper is to analyze these methods when they are combined with global strategies such as linesea rch techniques and model trust region algorithms. Most of the converge nce results are formulated for projection onto general subspaces rathe r than just Krylov subspaces.