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(a) f(x) Write a PYTHON function computing an approximation of the root p of the equation O using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = xn n = 0, 1, 2, ..., where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(xn) and |æn+1– xn|. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". xn < TOL for the first time, then return xn+1 as approximation of (b) Test code by finding an approximate solution to the equation log(x) + x = 0 your with an initial guess of our choice

(a) f(x) Write a PYTHON function computing an approximation of the root p of the equation O using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = xn n = 0, 1, 2, ..., where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(xn) and |æn+1– xn|. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". xn < TOL for the first time, then return xn+1 as approximation of (b) Test code by finding an approximate solution to the equation log(x) + x = 0 your with an initial guess of our choice

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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In this problem consider Newton's method. (a) f (x) Write a PYTHON function computing an approximation of the root p of the equation = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f (æn) f'(xn) Xn+1 = xn п %3D 0, 1, 2, ..., n = • •• . where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 – the root p. Allow the code to do only NMAX iterations. Xn < TOL for the first time, then return xn+1 as approximation of At every step n, the code should print the values n, xn, f (xn) and |xn+1 – xn|. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) with an initial guess of your choice. Test your code by finding an approximate solution to the equation log(x) + x = 0 2.
Transcribed Image Text:In this problem consider Newton's method. (a) f (x) Write a PYTHON function computing an approximation of the root p of the equation = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f (æn) f'(xn) Xn+1 = xn п %3D 0, 1, 2, ..., n = • •• . where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 – the root p. Allow the code to do only NMAX iterations. Xn < TOL for the first time, then return xn+1 as approximation of At every step n, the code should print the values n, xn, f (xn) and |xn+1 – xn|. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) with an initial guess of your choice. Test your code by finding an approximate solution to the equation log(x) + x = 0 2.
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