function NewtonRaphsonMethod %Implmentaton of Newton-Raphson method to determine a solution. %to approximate solution to x = cos(x), we let f(x) = x - cos(x) i = 1; p0 = 0.5*pi; %initial conditions N = 100; %maximum number of iterations error = 0.0001; %precision required syms 'x' f(x) = x - cos(x); %function we are solving df = diff(f); %differential of f(x) while i <= N p = p0 - (f(p0)/df(p0)); %Newton-Raphson method if (abs(p - p0)/abs(p)) < error %stopping criterion when difference between iterations is below tolerance fprintf('Solution is %f \n', double(p)) return end i = i + 1; p0 = p; %update p0 end fprintf('Solution did not coverge within %d iterations at a required precision of %d \n', N, error) %error for non-convergence within N iterations end
function NewtonRaphsonMethod%Implmentaton of Newton-Raphson
method to determine a solution.%to approximate solution to x =
cos(x), we let f(x) = x - cos(x)
i = 1;p0 = 0.5*pi; %initial conditionsN = 100; %maximum number
of iterationserror = 0.0001; %precision required
syms 'x'f(x) = x - cos(x); %function we are solvingdf = diff(f);
%differential of f(x)
