Newton-Raphson method is implemented here to determine the roots of a function. This algorithm is coded in MATLAB m-file. There are three files: func.m, dfunc.m and newtonraphson.m. The func.m defines the function, dfunc.m defines the derivative of the function and newtonraphson.m applies the Newton-Raphson method to determine the roots of a function.
#NewtonRaphson
Evaluating the root of sin(x):
func.m file
% defines the function as its roots to be determined
function [solution]=func(x)
solution=sin(x);
dfunc.m file
% defines the derivative of the function
function [dsolution]=dfunc(x)
dsolution=cos(x);
newtonraphson.m file
% applies Newton Raphson algorithm to determine the roots of a function
close all;
clear all;
x = input('Starting guess = ');
tolerance = 1e-8;
iterations = 0;
while (iterations<100) && (abs(func(x))>tolerance)
x = x-(func(x)/dfunc(x));
iterations = iterations + 1;
end
if iterations==100
disp('No root found')
else
disp(x)
end
Output:
Starting guess = 1
2.9236e-13
Starting guess = 0.1
1.2495e-11
Starting guess = 0.01
1.2335e-20
Evaluating the root of x-2*sin(xˆ2):
func.m file
% defines the function as it's roots to be determined
function [solution]=func(x)
solution = x-(2*sin(x.^2));
dfunc.m file
% defines the derivative of the function
function [dsolution]=dfunc(x)
dsolution=1-(4*x*cos(x));
Output:
Starting guess = 0.1
-1.0489e-10
Starting guess = 0.3
-2.4565e-10
Starting guess = 1
0.5055
Evaluating the root of x^2-5:
func.m file
% defines the function as it's roots to be determined
function [solution]=func(x)
solution = x^2-5;
dfunc.m file
% defines the derivative of the function
function [dsolution]=dfunc(x)
dsolution = (2*x);
Output:
Starting guess = 2
2.2361
Starting guess = 3
2.2361
Starting guess = 0.01
2.2361
#NewtonRaphson
