On the Convergence of Newton-Like Methods Based on M-Fréchet Differentiable Operators and Applications in Radiative Transfer
Tóm tắt
In this study we approximate a locally unique solution of a nonlinear operator equation in Banach space using Newton-like methods. A complete error analysis of our method is also given. Our new theorem uses Lipschitz or Hölder continuity assumptions on m-Fréchet-differentiable operators where m ≥ 2 is a positive integer. A numerical example is given to show that our results provide a better information on the location of the solution as well as finer error bounds on the distances involved than earlier results. A second numerical example shows how to solve a nonlinear integral equation appearing in radiative transfer.
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