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[ÇóÖú] СµÜÇó½Ì¼¸¸ö³ÌÐò-¹ØÓÚµü´ú·¨µÄ£¨¶àл£© ÒÑÓÐ1È˲ÎÓë

СµÜ±àдÁËTable4.1SORÖеÄr=0.01¼°n=8µÄ³ÌÐò£¬ÏÖÓÐÈçϼ¸¸öÒÉÎÊ£º1¡¢ÎÒÔËÐгöitΪ8£¬cpu=0.042£¬w(exp)=1.02£¬ÎªÊ²Ã´Óë×÷Õß²»Ò»Ñù£¿2¡¢×÷ÕßÖÕÖ¹Ìõ¼þÊÇF·¶Êý£¬ÎÒµÄÊÇ2·¶Êý£¬Ó¦¸ÃÔõôÐ޸ģ¿3.µ±n=64ʱ³öÏÖ¡®Out of memory. Type HELP MEMORY for your options.¡¯ÇëÎÊÊÇÎÒ³ÌÐòÌ«¸´ÔÓÁËÂð£¿
×¢£ºtestΪȷ¶¨w(exp)³ÌÐò£¬SORΪµ÷ÓóÌÐò£¬test2Ϊ¸ù¾Ýw(exp)¼ÆËãit³ÌÐò£¬¸÷λ´óÉñ²»Áߴͽ̡£
test.m:
n=8;
r=0.01;
a=ones(n,1);
b=ones(n-1,1);
I=eye(n);
MM=2*diag(a)-diag(b,-1)-diag(b,1);
N=0.5*diag(b,-1)-0.5*diag(b,1);
A=MM+2*r*N+100*I/(n+1);
B=A;
X=rand(n,n);
F=A*X+X*B;
E=kron(I,A)+kron(B',I);
b=F(;
%x=E\b;
x0=b;
ww=0.01:0.01:1.99;
D=diag(diag(E));    %ÇóEµÄ¶Ô½Ç¾ØÕó
L=-tril(E,-1);      %ÇóEµÄÏÂÈý½Ç¾ØÕó
U=-triu(E,1);       %ÇóEµÄÉÏÈý½Ç¾ØÕó
for i=1:length(ww)
    w=ww(i);
    B=inv(D-L*w)*((1-w)*D+w*U);
p(i)=max(max(abs(eig(B))));
%plot(ww,p);
[x,n1]=SOR(E,b,x0,w);
mm(i)=n1;
end
plot(ww,mm);
Xe=reshape(x,n,n);
errror=norm((Xe-X),2)

SOR.m:
function [x,n1]=SOR(E,b,x0,w,eps,M)

if nargin==4
    eps=1.0e-6;
    M=2000;
elseif nargin<4
    error
    return
elseif nargin==5
    M=200;
end
if(w<=0 || w>=2)    %ÊÕÁ²Ìõ¼þÒªÇó
    error;
    return;
end
D=diag(diag(E));    %ÇóEµÄ¶Ô½Ç¾ØÕó
L=-tril(E,-1);      %ÇóEµÄÏÂÈý½Ç¾ØÕó
U=-triu(E,1);       %ÇóEµÄÉÏÈý½Ç¾ØÕó
B=inv(D-L*w)*((1-w)*D+w*U);
f=w*inv((D-L*w))*b;
x=B*x0+f;
n1=1;               %µü´ú´ÎÊý
%µü´ú¹ý³Ì
while norm(x-x0)>=eps
    x0=x;
    x=B*x0+f;
    n1=n1+1;
    if(n1>=M)
        disp('Warining:µü´ú´ÎÊýÌ«¶à£¬¿ÉÄܲ»ÊÕÁ²£¡');
        return;
    end
end

test2.m
w=1.02
n=8;
r=0.01;
a=ones(n,1);
b=ones(n-1,1);
I=eye(n);
M=2*diag(a)-diag(b,-1)-diag(b,1);
N=0.5*diag(b,-1)-0.5*diag(b,1);
A=M+2*r*N+100*I/(n+1);
B=A;
X=rand(n,n);
F=A*X+X*B;
E=kron(I,A)+kron(B',I);
b=F(;
%x=E\b;
x0=b;
[x,n1]=SOR(E,b,x0,w)
Xe=reshape(x,n,n);
errror=norm((Xe-X),2)

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3Â¥: Originally posted by yanze at 2015-01-11 19:20:45
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Matlabר¼Ò

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