?? mulnewtonsor.m
字號:
function [r,m]=mulNewtonSOR(F,x0,w,h,l,eps)
if nargin==5
eps=1.0e-4;
end
n = length(x0);
J = zeros(n,n);
Fx = subs(F,findsym(F),x0);
for i=1:n
x1 = x0;
x1(i) = x1(i)+h(i);
J(:,i) = (subs(F,findsym(F),x1)-Fx)/h(i);
end
D = diag(diag(J));
L = -tril(J-D);
U = -triu(J-D);
inD = inv(D-w*L);
H = inD*(D - w*D+w*L);;
Hm = eye(n,n);
for i=1:l-1
Hm = Hm + power(H,i);
end
dr = w*Hm*inD*Fx;
r = transpose(x0)-dr;
m=1;
tol=1;
while tol>eps
x0=r;
Fx = subs(F,findsym(F),x0);
J = zeros(n,n);
for i=1:n
x1 = x0;
x1(i) = x1(i)+h(i);
J(:,i) = (subs(F,findsym(F),x1)-Fx)/h(i);
end
D = diag(diag(J));
L = -tril(J-D);
U = -triu(J-D);
inD = inv(D-w*L);
H = inD*(D - w*D+w*L);;
Hm = eye(n,n);
for i=1:l-1
Hm = Hm + power(H,i);
end
dr = w*Hm*inD*Fx;
r = x0-dr; %核心迭代公式
tol=norm(r-x0);
m=m+1;
if(m>100000) %迭代步數控制
disp('迭代步數太多,可能不收斂!');
return;
end
end
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