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Globally convergent algorithm for solving large nonlinear systems of equations. (English) Zbl 1071.65071

Author’s summary: An algorithm for solving large systems of nonlinear equations is introduced. The algorithm is a variant of the inexact Newton method where an approximate Newton direction is taken from a space of small dimension (Krylov subspace). The algorithm is based on the implicitly restarted Arnoldi method to construct a basis for the Krylov subspace in conjunction with a line search strategy to control the length of the step. It should cope quite well with large-scale systems of equations. A convergence theory for this algorithm is presented. It is shown that this algorithm is globally convergent. This theory is sufficiently general that it holds for any algorithm that projects the problem on a lower dimensional subspace.

MSC:

65H10 Numerical computation of solutions to systems of equations
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