matlab实现不动点迭代、牛顿法、割线法

不动点迭代

function xc = fpi( g, x0, tol )

    x(1) = x0;

    i = 1;

    while 1

        x(i + 1) = g(x(i));

        if(abs(x(i+1) - x(i)) < tol)

            break

        end

        i = i + 1;

    end

    xc = x(i+1);

end

牛顿法：

function xk = funNewton(f, x0, max_steps, tol)

    syms x

    symbol_f = f(x);

    dif_f = matlabFunction(diff(symbol_f));

    clear x

    x = x0;

    for k = 1:max_steps

       xk = x;

       disp(['the ', num2str(k), ' time is ', num2str(x)])

       %xk to save the last time value of x

       x = x - f(x) / dif_f(x);

       %newton solve

       if(abs(xk - x) < tol)

       %decide whether to break out

            break;

       end

    end

end

割线法：

function xc = CutLine( f, x0, x1, tol )

    x(1) = x0;

    x(2) = x1;

    i = 2;

    while 1

        x(i + 1) = x(i) - (f(x(i)) * (x(i) - x(i - 1))) / (f(x(i)) - f(x(i - 1)));

        if(abs(x(i + 1) - x(i)) < tol)

            break;

        end

        i = i + 1;

    end

    xc = x(i + 1);

end

Stewart平台运动学问题求解：

function out = Stewart( theta )

    % set the parameter

    x1 = 4;

    x2 = 0;

    y2 = 4;

    L1 = 2;

    L2 = sqrt(2);

    L3 = sqrt(2);

    gamma = pi / 2;

    p1 = sqrt(5);

    p2 = sqrt(5);

    p3 = sqrt(5);

    % calculate the answer

    A2 = L3 * cos(theta) - x1;

    B2 = L3 * sin(theta);

    A3 = L2 * cos(theta + gamma) - x2;

    B3 = L2 * sin(theta + gamma) - y2;

    N1 = B3 * (p2 ^ 2 - p1 ^ 2 - A2 ^ 2 - B2 ^ 2) - B2 * (p3 ^ 2 - p1 ^ 2 - A3 ^ 2 - B3 ^ 2);

    N2 =  -A3 * (p2 ^ 2 - p1 ^ 2 - A2 ^ 2 - B2 ^ 2) + A2 * (p3 ^ 2 - p1 ^ 2 - A3 ^ 2 - B3 ^ 2);

    D = 2 * (A2 * B3 - B2 * A3);

    out = N1 ^ 2 + N2 ^ 2 - p1 ^ 2 * D ^ 2;

end

test our function at theta = - pi / 4 and theta = pi / 4

clear all

clc

format short

disp('f(- pi / 4) is ')

out1 = Stewart(- pi / 4)

disp('--------------')

disp('f(pi / 4) is ')

out2 = Stewart(pi / 4)