newton_raphson.m

clc
clear

f = @(x) x^3 - 2*x;
fprime = @(x) 3*x^2 - 2;
tolerancetarget = 10^-7;
epsilon = 10^-16;
found_soln = false;
maxIterations = 30;
x0(1) = 1000;

for i = 1:maxIterations
    y(i) = f(x0(i));
    yprime(i) = fprime(x0(i));

    if(abs(yprime(i))<epsilon)
        fprintf("Denominator is too smaLL");
        break;
    end

    x1(i) = x0(i) - y(i)/yprime(i);

    tolerance(i) = abs(x1(i)-x0(i))/abs(x1(i));

    if(tolerance(i)<tolerancetarget)
        found_soln = true;
        break;
    end

    x0(i+1) = x1(i);

    h1(i) = subplot(221);
    set(h1(i),'XLim',[0 maxIterations],'YLim',[0 x0(1)])
    plot(i,x1(i),'r-*')
    grid on
    xlabel('Number of Iterations')
    ylabel('Solution Value')
    hold on

    h2(i) = subplot(222);
    set(h2(i),'XLim',[0 maxIterations],'YLim',[0 tolerance(1)])
    plot(i,tolerance(i),'b-*')
    grid on
    xlabel('Number of Iterations')
    ylabel(' Calculated Tolerance')
    hold on
end
if (found_soln) % We found a solution within tolerance and maximum number of iterations
    fprintf('The root is: %f\n', x1);
else %If we weren't able to find a solution to within the desired tolerance
    fprintf('Warning: Not able to find solution to within the desired tolerance of %f\n', tolerancetarget);
    fprintf('The last computed approximate root was %f\n', x1)
end

set(1, 'units', 'centimeters', 'pos', [0 0 120.5 100])