Consider the function f(x)=4x-1-sin(x) on the interval 0≤x≤2. Perform 4 iterations of Newton’s Method on f(x) with the initial guess x0=1. Show xn and f(xn) at each step. Perform 4 iterations of Secant Method on f(x) using the end points of the interval as initial data. Show the new estimate xn and f(xn) at each step.
Consider the function f(x)=4x-1-sin(x) on the interval 0≤x≤2. Perform 4 iterations of Newton’s Method on f(x) with the initial guess x0=1. Show xn and f(xn) at each step. Perform 4 iterations of Secant Method on f(x) using the end points of the interval as initial data. Show the new estimate xn and f(xn) at each step.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 20EQ
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Consider the function f(x)=4x-1-sin(x) on the interval 0≤x≤2.
- Perform 4 iterations of Newton’s Method on f(x) with the initial guess x0=1. Show xn and f(xn) at each step.
- Perform 4 iterations of Secant Method on f(x) using the end points of the interval as initial data. Show the new estimate xn and f(xn) at each step.
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