I am writing a MATLAB program that has to dfo the following. Use (a) the Newtoni

ID: 2997675 • Letter: I

Question

I am writing a MATLAB program that has to dfo the following.

Use (a) the Newtonian-Raphson method and (b) the modified secant method (=0.05) to determine the root of f(x) using an intial guess of x = 0.5825 and ?s = 0.01%. Explain your results.

This is what I have so far, but it doesn't work. Any help would be appreciated. Thanks

The function file is as follows:

function [x,y,n]=newtrapf(fn,gn,xl,tol,max)

% Function to find the root of a function fn using the false-position method

%Inputs are:-

% fn gn = funtion and derivative names in quotes, respectively

% xl = guesses which bracket the root

% tol = tolerance level

% max = maximum number of iterations allowed

%Outputs are:-

% x => desired root

% y => error in calculating root

% n => number of iterations

n=0;

error=1;

errora=1000;x=1000;

while errora > tol

fl=feval(fn,xl);

gl=feval(gn,xl);

xr=xl-fl/gl;

fr=feval(fn,xr);

xold=x;

xl=xr;y=fr;

x=xr;

errora=abs((x-xold)/(x+eps)*100);

error=abs(y);

n=n+1;

if n >= max

disp('Warning! Maximun number of iterations reached but not converged yet!')

break

end

The command lines are as follows:

syms x

fn=@(x)x^5-16.05*x^4+88.75*x^3-192.0375*x^2+116.35*x-31.6875;

gn=@(x)5*x^4-(321*x^3)/5+(1065*x^2)/4-(15363*x)/40+2327/20;

[x,y,n]newtrapf(fn,gn,0.5825,0.0001,3)

Explanation / Answer

% one end command was missing.