Question

Using the bisection method:
    Make a program to use this method using the following three functions and use it to find the root of this function f (x) = x * x * x-8.
a) A function so that the user between xlower and xupper that meets the value of the function has a different sign and if he does not ask for new values.
b) A function to find the root and call it bisection and perform a maximum of iterations (maximum approximations of the root). All estimated root values have to be printed.
c) A function to obtain the values of the function.

Answer 1

%%Matlab code for finding root using newton secant bisection and false
clear all
close all

%function for which root have to find
fun=@(x) x.*x.*x-8;

xx=linspace(-2,3);
yy=fun(xx);

plot(xx,yy)
xlabel('x')
ylabel('f(x)=x^3-8')
title('x vs. f(x) plot')

[root]=bisection_method(fun,-2,3,1000);
fprintf('\tRoot using Bisection method is %f.\n',root)
hold on
plot(root,fun(root),'r*')

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%Matlab function for Bisection Method
function [root]=bisection_method(fun,x0,x1,maxit)
if fun(x0)<=0
    t=x0;
    x0=x1;
    x1=t;
end
fprintf('\nRoot using Bisection method\n')
%f(x1) should be positive
%f(x0) should be negative
k=10; count=0;
while k>5*10^-10
    count=count+1;
    xx(count)=(x0+x1)/2;
    mm=double(fun(xx(count)));
    if mm>=0
        x0=xx(count);
    else
        x1=xx(count);
    end
    err(count)=abs(fun(x1));
    k=abs(fun(x1));
    if count>=maxit
        break
      
    end
    %
end
fprintf('\tAfter %d iteration root using Bisection method is %f\n',count,xx(count))
root=xx(end);
end

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