Question

Write a MATLAB function newtonRaphson(fx, x0, sigfig, maxIT) that will return a root of the function f(x) near x=x0 using the Newton-Raphson method, where sigfig is the accuracy of the solution in terms of significant figures, and maxIT is the maximum number of iterations allowed. In addition to the root (xr), the function newtonRaphson is expected to return the number of iterations and an error code (errorCode). As such, the first line of the function m file newtonRaphson.m must read as: function [xr, nIT, errorCode] = newtonRaphson(fx, x0, sigfig, maxIT)

Answer 1

%the function script is

function [xr nIT errorCode]=newtonRaphson(f,x0,sigfig,maxit)
syms x
dfn =diff(f,x);
df=inline(dfn,'x');
for i=1:maxit
    x(i)=x0-f(x0)/df(x0);
    tol1(i)=abs(x(i)-x0);
    x0=x(i);
    
   nIT=i;
   xr=double(x(i));
     errorCode=double(tol1(i));
   if tol1(i)<sigfig
       break;
   end
end

%the input script for calling function is

clc;clear all;
f = @(x) x^2-4*x-7;
x0=5;
format short
sigfig=0.0001;
maxit=100;
[xr nIT errorCode]=newtonRaphson(f,x0,sigfig,maxit)

%output

DesktoP Command Window xr = 5.3166 errorCode 4.1876e-05 fx >