matlab求解矩阵方程组 matlab求矩阵方程组
\u7528matlab\u89e3\u77e9\u9635\u65b9\u7a0b\u7ec4\u7684\u4ee3\u7801\u600e\u4e48\u5199\uff1f\u5148\u5c06xP=0\u4e24\u8fb9\u53d6\u8f6c\u7f6e\uff0c\u5f97P'x'=0,\u6c42\u51fax'\u518d\u8f6c\u7f6e\u56de\u6765\u6c42\u51fax.
\u5f53\u77e9\u9635\u65b9\u7a0bP'x'=0,rank(P)=r<n\u65f6,\u5373P\u662f\u5947\u5f02\u7684\uff0c\u8fd9\u65f6\u65b9\u7a0b\u6709\u65e0\u7a77\u591a\u4e2a\u89e3,\u7528MATLAB\u53ef\u6c42\u51fa\u5b83\u7684\u4e00\u4e2a\u57fa\u672c\u89e3\u7cfb\uff0c \u57fa\u672c\u89e3\u7cfb\u7684\u7ebf\u6027\u7ec4\u5408\u5c31\u662f\u5b83\u7684\u901a\u89e3\uff08\u4e00\u822c\u89e3\uff09
\u800c\u6c42\u57fa\u672c\u89e3\u7cfb\u7528matlab \u4e2d\u7684\u547d\u4ee4 x=null(P', r )\u5373\u53ef.\u5176\u4e2d:r=rank(P).
\u91cd\u65b0\u6574\u7406\u4e00\u4e0b\u4f60\u7684\u65b9\u7a0b\u3002
\u4f60\u7684\u7b2c\u4e00\u4e2a\u65b9\u7a0b\u662f
\uff08pi0,pi1\uff09=(pi0,pi1)*[A00,A01;A10,R*A2]
\u53d6\u4e2a\u8f6c\u7f6e\uff0c\u5c31\u662f
\uff08pi0,pi1\uff09(T)
=
[A00,A10;A01,R*A2]*(pi0,pi1)(T)
\u76f8\u5f53\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4
Ax
=
0
A
=
[A00
-
1,A10;A01,R*A2
-
1]
x
=
(pi0,pi1)(T)
\u4f60\u8fd8\u6709\u4e00\u4e2a\u7ea6\u675f\u6761\u4ef6\uff0c\u5bf9\u5427\uff1a
1=pi0*e+pi1*inv(I-R)*e;
\u8fd9\u76f8\u5f53\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u7b2c\u4e09\u884c\u3002
\u6240\u4ee5\u76f8\u5f53\u4e8e\uff1a
//
\u4ee3\u7801\u5982\u4e0b
A
=
[A00
-
1,A10;
A01,R*A2
-
1;
e,*inv(I-R)*e];
b
=
[0;
0;
1];
x
=
A\b;
//
Matlab\u81ea\u52a8\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u8bed\u53e5\uff0c\u6ca1\u8bb0\u9519\u7684\u8bdd\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u8d85\u5b9a\u65b9\u7a0b\u7ec4\uff0c\u5e94\u8be5\u4e5f\u80fd\u81ea\u52a8\u641e\u5b9a\uff0c\u7b97\u51fa\u6700\u5c0f\u4e8c\u4e58\u89e3
//
\u4ee3\u7801\u7ed3\u675f
\u6700\u540e\uff0c\u6c42\u51fa\u6765\u7684x\u662f\u4e2a2*1\u7684\u5411\u91cf\uff0c\u4e24\u4e2a\u5206\u91cf\u5206\u522b\u5bf9\u5e94pi0\u548cpi1
\u4f60\u8bd5\u8bd5\u5427
题主的问题可以用for双循环语句和solve（或vpasolve）函数求出FI(i)、GI(i)的值。实现方法：
k=1;
for i=1:4
for j=1:4
syms FI0、GI0
[FI0,GI0]=vpasolve(FI0*dGI(i,j)-GI0*dSI(i,j)==0,FI0*dSI(i,j)-GI0*dGI(i,j)==0)
FI(k)=FI0,GI(k)=GI0
k=k+1;
end
end
绛旓細matlab姹傜嚎鎬ф柟绋嬬粍閭ｄ箞蹇湁浠ヤ笅鍘熷洜锛1銆佷紭鍖栫畻娉曪細MATLAB鍐呴儴瀹炵幇浜嗗绉嶉珮鏁堢殑绾挎ф柟绋嬬粍姹傝В绠楁硶銆傛牴鎹緭鍏ョ殑鐭╅樀绫诲瀷鍜屽ぇ灏忥紝MATLAB浼氳嚜鍔ㄩ夋嫨鏈鍚堥傜殑绠楁硶鏉ユ眰瑙ｆ柟绋嬬粍锛屼粠鑰屾彁楂樿绠楁晥鐜囥2銆佺█鐤忕煩闃垫敮鎸侊細瀵逛簬绋鐤忕煩闃碉紙鐭╅樀涓ぇ閮ㄥ垎鍏冪礌涓洪浂锛夌殑绾挎ф柟绋嬬粍姹傝В锛孧ATLAB閲囩敤浜嗕笓闂ㄤ紭鍖栫殑绠楁硶锛屽埄鐢ㄧ█鐤忕煩...
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