以下の４元連立非線形方程式を解く。
clear; close all; syms f(x,y,u,v) g(x,y,u,v) h(x,y,u,v) k(x,y,u,v) f(x,y,u,v) = x^3-3*x*y^2 ... +3*((x^2-y^2)*u-2*x*y*v)... +3*((u^2-v^2)*x-2*u*v*y)... +u^3-3*u*v^2 ... +6*(x^2-y^2+2*(x*u-y*v)+u^2-v^2)... +21*(x+u)+32; g(x,y,u,v) = 3*x^2*y-y^3 ... +3*(2*x*y*u+(x^2-y^2)*v) ... +3*(2*u*v*x+(u^2-v^2)*y) ... +(3*u^2*v-v^3) ... +6*(2*x*y+2*(y*u+x*v)+2*u*v) ... +21*(v+y); h(x,y,u,v) = x^2-y^2-u^2+v^2-1; m(x,y,u,v)= 2*x*y-2*u*v-1; J = jacobian([f,g,h,m],[x,y,u,v]); J1 = inv(J); x=zeros(1,10); y=zeros(1,10); u=zeros(1,10); v=zeros(1,10); delta=1e-8; res=1e4; x(1)=-1; y(1)=-2; u(1)=-1; v(1)=2; k=1; while res>delta^2 next = [x(k);y(k);u(k);v(k)] ... - J1(x(k),y(k),u(k),v(k)) * ... [f(x(k),y(k),u(k),v(k)); g(x(k),y(k),u(k),v(k)); h(x(k),y(k),u(k),v(k)); m(x(k),y(k),u(k),v(k))] ; x(k+1) = next(1); y(k+1) = next(2); u(k+1) = next(3); v(k+1) = next(4); res = (f(x(k+1),y(k+1),u(k+1),v(k+1)))^2 ... + (g(x(k+1),y(k+1),u(k+1),v(k+1)))^2 ... + (h(x(k+1),y(k+1),u(k+1),v(k+1)))^2 ... + (m(x(k+1),y(k+1),u(k+1),v(k+1))^2); disp(eval(res)); k=k+1; end fprintf('ans\n x = %f\n y = %f\n u = %f\n v = %f\n',x(k),y(k),u(k),v(k));
計算結果
ans x = -1.508467 y = -0.189549 u = -1.129368 v = 0.189549
