最速下降法--MATLAB程序

function x = fxsteep(f,e,a,b) x1 = a; x2 = b; Q = fxhesson(f,x1,x2); x0 = [x1,x2]; temp = [x0]; fx1 = diff(f,x1); fx2 = diff(f,x2); g = [fx1,fx2]; g1 = subs(g); d = - g1; while (abs(norm(g1))> e) lamda = (-d)*d/((-d)*Q*d); x0 = x0 - lamda *g1; temp = [temp;x0]; a = [1,0] * x0; b = [0,1] * x0; x1 = a; x2 = b; g1 = subs(g); d = - g1; end x = temp; end

function Q = fxhesson(f,a,b) x1 = a; x2 = b; fx1 = diff(f,1,x1); fx2 = diff(f,1,x2); fx1x1 = diff(fx1,1,x1); fx1x2 = diff(fx1,1,x2); fx2x2 = diff(fx2,1,x2); fx2x1 = diff(fx2,1,x1); fx1x1 = subs(fx1x1); fx1x2 = subs(fx1x2); fx2x1 = subs(fx2x1); fx2x2 = subs(fx2x2); Q = [fx1x1,fx1x2;fx2x1,fx2x2];

end

syms x1 x2; X=[x1,x2]; fx=X(1)^2+4*X(2)^2; z=fxsteep(fx,0.0001,1,1)

ans

1 1 48/65 -3/65 36/325 36/325 1728/21125 -108/21125 1296/105625 1296/105625 62208/6865625 -3888/6865625 46656/34328125 46656/34328125 2239488/2231328125 -139968/2231328125 1679616/11156640625 1679616/11156640625 80621568/725181640625 -5038848/725181640625 60466176/3625908203125 60466176/3625908203125 2902376448/235684033203125 -181398528/235684033203125

function x = fxsteep(f,e,a,b) x1 = a; x2 = b; Q = fxhesson(f,x1,x2); x0 = [x1,x2]; temp = [x0]; fx1 = diff(f,x1); fx2 = diff(f,x2); g = [fx1,fx2]; g1 = subs(g); d = - g1; while (abs(norm(g1))> e) lamda = (-d)*d/((-d)*Q*d); x0 = x0 - lamda *g1; temp = [temp;x0]; a = [1,0] * x0; b = [0,1] * x0; x1 = a; x2 = b; g1 = subs(g); d = - g1; end x = temp; end function Q = fxhesson(f,a,b) x1 = a; x2 = b; fx1 = diff(f,1,x1); fx2 = diff(f,1,x2); fx1x1 = diff(fx1,1,x1); fx1x2 = diff(fx1,1,x2); fx2x2 = diff(fx2,1,x2); fx2x1 = diff(fx2,1,x1); fx1x1 = subs(fx1x1); fx1x2 = subs(fx1x2); fx2x1 = subs(fx2x1); fx2x2 = subs(fx2x2); Q = [fx1x1,fx1x2;fx2x1,fx2x2]; end syms x1 x2; X=[x1,x2]; fx=X(1)^2+4*X(2)^2; z=fxsteep(fx,0.0001,1,1) ans 1 1 48/65 -3/65 36/325 36/325 1728/21125 -108/21125 1296/105625 1296/105625 62208/6865625 -3888/6865625 46656/34328125 46656/34328125 2239488/2231328125 -139968/2231328125 1679616/11156640625 1679616/11156640625 80621568/725181640625 -5038848/725181640625 60466176/3625908203125 60466176/3625908203125 2902376448/235684033203125 -181398528/235684033203125