Write a MATLAB function, called bisection_method that inputs a function f, two n

Question

Write a MATLAB function, called bisection_method that inputs a function f, two numbers a, b, an error tolerance, tol, and a maximum number of iterations, N, and finds a root c of f in the interval [a, b using the bisection method. Your function should compute a bound on the error, and stop when the error is less than the tolerance, or if the number of iterations exceeds N whichever happens first. (a) Hint #1: The function should start with the line function [c,n,err] bisection, method ( f , a, b, tol,N) = (b) Hint #2: The function should contain a"while, loop, looking something like: while err tol && n

Explanation / Answer

PLEASE CREATE bisection_method.m AND PASTE BELOW CODE

function [c,n,err] = bisection_method(f,a,b,tol,N)

% Check that that neither end-point is a root

% and if f(a) and f(b) have the same sign, throw an exception.

if( f(a) == 0)

c = a;

n = 0;

err = 0;

return;

elseif(f(b) == 0)

c = b;

n = 0;

err = 0;

return;

elseif(f(a) * f(b) > 0)

error('f(a) and f(b) do not have opposite sign');

end

% We will iterate N times and if a root was not

% found after N iterations.

err = 0.1;

n = 1;

while err > tol && n < N

m = (a+b)/2;

% Check if we found a root or whether or not

% we should continue with:

% [a, m] if f(a) and f(m) have opposite signs, or

% [m, b] if f(m) and f(b) have opposite signs.

if( f(m) == 0 )

c = m;

err = 0;

return;

elseif( f(m) * f(a) < 0 )

b = m;

else

a = m;

end

  

if( b - a < tol)

if(abs(f(a)) < abs(f(b)))

c = a;

err = b - a;

return;

else

c = b;

err = b - a;

return;

end

end

n = n + 1;

end

error( 'the method did not converge' );

end

CREATE test.m AND PASTE BELOW CODE

close all

clear all

clc

syms x

f = @(x)(2*x^3 + 3 * x - 1) * cos(x) -x;

a = -1;

b = 1;

tol = 10^-5;

N = 100000;

[c,n,err] = bisection_method(f,a,b,tol,N)

c = fzero(f,[-1,1])

PLEASE REFER BELOW OUTPUT

c =

0.4386

n =

18

err =

7.6294e-06

c =

0.4386

>>

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.