Volume 19, Issue 6
Picard Iteration for Nonsmooth Equations
DOI:

J. Comp. Math., 19 (2001), pp. 583-590

Published online: 2001-12

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• Abstract

This paper presents an analysis of the generalized Newton method,approximate Newton methods, and splitting methods for solving nonsmooth equations from Picard iteration viewpoint. It is proved that the radius of the weak Jacobian (RGJ) of Picard iteration function is equal to its least Lipschitz constant. Linear convergence of superlinear convergence results can be obtained provided that RGJ of the Picard iteration function at a solution point is less than one or equal to zero. As for applications, it is pointed out that the approximate Newton methods, the generalized Newton method for piecewise C_1 problems and splitting methods can be explained uniformly with the same viewpoint.

• Keywords

Nonsmooth equations Picard iteration Weak Jacobian Convergence