Question

Write functions for the specified root finding methods. Include a comments in each function that notes the inputs and outputs. Use Cody Coursework to help guide writing your functions. You may not use built-in MATLAB methods for root-solving such as fzero.l] Part A: Write a function that implements the bisection method for root-finding. Part B: Write a function that implements the secant method for root-finding

Answer 1

MATLAB Code:

close all
clear
clc

tol = 1e-6;
fun = @(x) 54*x^6 + 45*x^5 - 102*x^4 - 69*x^3 + 35*x^2 + 16*x - 4;

% Root in the Interval (-1.5, -1)
root_bisect = bisect(fun, -1.5, -1, tol)
root_secant = secant(fun, -1.5, -1, tol)

function xc = bisect(f,a,b,tol)
if sign(f(a)) * sign(f(b)) >= 0
error('f(a)f(b) < 0 not satisfied!')
end
fa = f(a);
fb = f(b);
while (b - a)/2 > tol
c = (a + b)/2;
fc = f(c);
if abs(f(c)) < tol
break
end
if sign(fc) * sign(fa) < 0
b = c; fb = fc;
else
a = c; fa = fc;
end
end
xc = (a + b)/2;
end

function xc = secant(f,a,b,tol)
while true
c = (b*f(a) - a*f(b)) / (f(a) - f(b));
if abs(f(c)) < tol
break
end
if f(a)*f(c) < 0
b = c;
else
a = c;
end
end
xc = c;
end

Output:

root_bisect =
-1.3813
root_secant =
-1.3813