Concerning the radius of convergence of Newton’s method and applications
Copyright policy )Concerning the radius of convergence of Newton’s method and applications
This paper deals with the problem of approximating a local unique solution of a twice continuously Fréchet-differentiable operator defined on an open convex subset of a Banach space. The author presents local and semilocal convergence results for Newton's method. In particular, using Lipschitz-type assumptions on the second Fréchet-derivative the author finds results concerning the radius of convergence of this method. Some numerical examples are presented.
- Cameron University United States
numerical examples, Newton's method, Banach space, convergence, Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, affine invariant operator
numerical examples, Newton's method, Banach space, convergence, Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, affine invariant operator
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