Question

Programming Language: MATLAB

Problem 3: (5 Points) Write a function with the header: function [R] -myNewtonRaphson (f, fp, x0, tol) which takes as input f: a function handle fp: a function handle to the derivative of f (note how I do it in the test case). x0: the initial guess of the root tol: a tolerance above which the algorithm will keep iterating. Tips: . Be sure to include an iteration counter which will stop the while-loop if the number of iterations get greater than 1000 It is not necessary to print out a convergence table within the while loop. (l.e., there should be no fprintf statements in your code) Test Case: >> format longg fQ(x) 2* (1-cos (x) )+4* (1-sqrt (1- (0.5*sin(x)) .*2)) - 1.2; >>df Q(x) (f (x 1e-8) - f (x) / 1e-8; >>[root, nIter]myNewtonRaphson (f, df ,1, 1e-8) root 0.958192178746275 nIter

Answer 1

function [R,i]=myNewtonRaphson(f,fp,x0,tol)
i=1;
while abs(f(x0))>tol && i<1000
    x0=x0-f(x0)/fp(x0);
    i=i+1;
end
R=x0;

>>format long >>f-e (x) 2* (1-cos (x))+4 (1-srt (1-(.5 sin(x))- *2))-1.2; >>df-e (x) (f (xtle-8)-f (x))/le-8: >[root,nIter]-myNewtonRaphson (f,df,1,le-8) r1-myievtonRaphson (,d root = 0.958192178746275 nIter - x >