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Globally convergent inexact quasi-Newton methods for solving nonlinear systems. (English) Zbl 1034.65032
A globally convergent inexact quasi-Newton method for numerically solving systems of nonlinear equations is described and analyzed. The algorithm combines the inexact Newton method with a non-monotone technique similar to one used for obtaining global convergence of Broyden’s method. The amount of reduction required at each iteration is proportional to the residual norm. Under additional standard assumptions also superlinear convergence is obtained.

65H10 Numerical computation of solutions to systems of equations
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