Question

Problem 4 (programming): Create a MATLAB function named mynewton.m to estimate the root for any arbitrary function f given an initial guess xo, an absolute error tolerance e and a maximum number of iterations max iter. Follow mynewton.m template posted in homework 2 folder on TritonED for guidance. You are not required to use the template. The function should return the approximated root ^n and the number of steps n taken to reach the solution. Use function mynewton.m to perform the following exercises. (a, b) Find the root of f(x32 36z+31 with zo 1.5, 10-3 and a maximum number of iterations equal to 25. Put the root in p4a and the corresponding number of steps in p4b. (c, d) Find the root of f(x 23+3z2-36x+31 with zo 2, 10-3 and a maximum number of iterations equal to 250. Put the root in p4c and the corresponding number of steps in p4d. function [xn, n] mynewt on (f, fp, x0, epsilon, maxiter) % MYNEWTON : solves for the root of f(x) = 0 using Newton's method. % Inputs are anonymous function f, anonymous function fp for % the derivative, initial guess x0, error tolerance epsilon and the maximum % number of iterations max-iter. Outputs are the approximated root xn and the number of iterations n taken. % Call format: [xn, n] -mynewton(f, fp, x0, epsilon, maxiter) % Initialize: E while n

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

close all
clear all
clc
f=@(x) 2*x^3+3*x^2-36*x+31;
fp=@(x) 6*x^2+6*x-36;
x0=1.5;
epsilon=1e-3;
max_iter=25;
[p4a,p4b]=mynewton(f,fp,x0,epsilon,max_iter)
x0=2;
epsilon=1e-3;
max_iter=250;
[p4c,p4d]=mynewton(f,fp,x0,epsilon,max_iter)
function [xn,n]=mynewton(f,fp,x0,epsilon,max_iter)
n=0;
xn=x0;
while(n<=max_iter)
xn=x0-f(x0)/fp(x0);
x0=xn;
  
n=n+1;
if(abs(f(x0))<epsilon)
break;
end
end
  
end

MATLAB R2018a EDITOR ② ▼| rch Documentation Log In Find Files Compare Print Run Section New Open Save Advance Run and Find Indent Advance C: Users PRADEEP KALRA 、Documents MATLAB Current Folder Editor-CAUsers\PRADEEP KALRA TLABsaveee.m Name pradeep.m xlnewtonrapsonsbypradeep.m x linterp poly.m+ saveee.m × E mathlab S- fp-@{x)6"Х"2+6*x-36; 6-x0-1.5 7-epsilon-1e-3 8ax_iter-25: 9-[p4a,p4blynerton (f, fp,x0,epsilon,max in New folder iter) 10-x0-2: epsilon-1e-3: a4.m a5.m A1.dat A1.mat A2.dat A3.dat 12max iter-250: pic,D4d mymerton (f, fp, x0,epsilon, max iter) Command Window New to MATLAB? See resources for Getting Started Name ▲ Value 1.0000e-03 @(x)2"X ^ 3+ 3"х ^2-36..' (x)6x 2+6x-36 250 1.0000 P4c max iter NaN 251 251 p4d x0 2 usages of "p4b found Ln 13 Coll 9 O Type here to search ENG 1:41 PM yA ^ 4) IN 04/16/19

Kindly revert for any queries

Thanks.