Numerical Functional Analysis and Optimization · 1994 · 13 citations · 10 references
ComputingComputer ScienceDifferential EquationsConvergence AnalysisIterative SolversNumerical AlgorithmsNumerical ConvergenceNumerical Methods For Differential EquationsOperator TheoryConvergenceLipschitz ConditionsLipschitz ContinuityNewton ConvergenceNewton's Method As A Fixed Point ProcessNonlinear Convergence Analysis
Convergence analysis of iterative methods for solving operator equations in Banach spaces depends on the smoothness degree of operators involved. We introduce and study a new smoothness assumption, more general and more flexible than the traditional Lipschitz smoothness. The analysis of Newton's method based on this assumption yields stronger results than those provided by the currently available theory.
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On the approximate solution of operator equations
Ken S. Thomas · Numerische Mathematik · 1974 · 312 citations