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)