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Global inexact Newton methods for very large scale nonlinear problems. (English) Zbl 0745.65032
For very large scale nonlinear problems $$F(x)=0$$, $$f: D\subset\mathbb{R}^ n\to\mathbb{R}^ n$$, $$F\in C^ 1(D)$$ the paper discusses algorithms which use the Newton method as outer iteration and iterative methods for the linearized problems as inner iteration. To maintain the high convergence of Newton method under the accuracy required in the inner iteration and to reduce the computational effort, the author combines the concept of inexact Newton methods with that of affine invariant exact Newton methods and introduces an automatic damping strategy, a cheaply implementable and effective matching strategy for termination criteria of the inner and outer iterations. Efficient implementation of the proposed algorithm is demonstrated by numerical examples.
Reviewer: Z.Mei (Marburg)

##### MSC:
 65H10 Numerical computation of solutions to systems of equations
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