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Fixed Point and Newton Method Analysis by Surya Tk is a document available to read on EtoBox.
(1) Find a fixed point of a function g(x) by showing it is a contraction mapping on a bounded set Dα. Use this to find an initial rectangle containing the fixed point and perform one Newton step. (2) Consider the secant method for finding roots of a function f(x). View it as an inexact Newton method and use results on inexact Newton convergence to bound the error at step k+1 in terms of the errors at steps k and k-1.
- Author
- Surya Tk
- Language
- EN