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Convergence theory of nonlinear Newton-Krylov algorithms. (English) Zbl 0814.65048
The variant of Newton’s iteration, where the approximate Newton direction is taken from a space of small dimension, is used in conjunction with a Krylov subspace method for solving the Jacobian linear systems. The main focus of this paper is to analyze these methods when they are combined with global strategies such as line search techniques and model trust region algorithms. Most of the convergence results are formulated for nonlinear Krylov subspace methods.

65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
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