Intersection of a linear and a non linear equation with Newton Raphson method

Question

Patrick Rohrmoser 2020-11-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/638310-intersection-of-a-linear-and-a-non-linear-equation-with-newton-raphson-method

评论： Patrick Rohrmoser 2020-11-6

Hey guys,

I have this function. I would like to find the intersection between two functions. So when I plot the functions I can see my non linear function and the intersection point, but instead of plotting the linear function I have just a constant.

I hope you can help finding the root cause of my problem.

Thank you so much in advance!

This is the function that I use:

function [root] = function_newton_raphson(func, diff, x0, maxIteration, xMin, xMax, a, b)
x = x0;
root = 0;
Epsilon = 1e-6;
linear = a*x+b;
for i = 1:maxIteration 
    if diff(x(i)) < Epsilon
        fprintf('Pitfall has occured. Try another initial guess\n')
        return;
    end
    
    x(i+1) = x(i) - (func(x(i))-a*x(i)-b)/(diff(x(i))-a);
    abs_error(i+1) = abs((x(i+1)-x(i))/x(i+1))*100;
    if abs(x(i+1)-x(i)) < Epsilon
        fprintf('The root has converged at x = %.10f\n', x(i+1));
        root = x(i+1);
        fplot(func, [xMin xMax])
        hold on;
        title('$ $ Newton-Raphson method to find intersection of f(x)', 'Interpreter', 'latex');
        fplot(linear, [xMin xMax])
        plot(root, linear, '*');
        text(root, linear, '\leftarrow intersection WP');
        legend(func2str(func));
        grid on;
        break;
    else
        fprintf('Iteration no: %d, current guess x = %.10f, error = %.5f\n', i, x(i+1), abs_error(i+1));
    end   
end
end

And I call it like this in the editor

func = @(x) 2*x.^2;
diff = @(x) 4*x;
x = function_newton_raphson(func, diff, 1.6, 50, 0, 5, 2, 1)
y = func(x)

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Answer 1

Alan Stevens 2020-11-6

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/638310-intersection-of-a-linear-and-a-non-linear-equation-with-newton-raphson-method#answer_536185

在 MATLAB Online 中打开

Change

linear = a*x+b;

to

linear = @(x) a*x+b;

and

        plot(root, linear, '*');
        text(root, linear, '\leftarrow intersection WP');

to

        plot(root, linear(root), '*');
        text(root, linear(root), '\leftarrow intersection WP');

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Alan Stevens 2020-11-6

This is what I get with the changes I suggested

Patrick Rohrmoser 2020-11-6

Thank you so much for your help!

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Intersection of a linear and a non linear equation with Newton Raphson method

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Intersection of a linear and a non linear equation with Newton Raphson method

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