MATLAB怎么利用fsolve求解矩阵方程 MATLAB中fsolve如何求解n多个代数方程组
\u8bf7\u6559\uff0cMatlab\u7684fsolve\u51fd\u6570\u600e\u4e48\u7528fsolve\u662f\u91c7\u7528\u6700\u5c0f\u4e8c\u4e58\u6cd5\u6765\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u3002\u5b83\u7684\u4e00\u822c\u6c42\u89e3\u65b9\u5f0f\u4e3a\uff1a
X=fsolve(fun,X0,options)
\u5176\u4e2d\uff0cfun\u662f\u8981\u6c42\u89e3\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\uff0cX0\u662f\u53d8\u91cf\u521d\u503c\uff0coptions\u7531optimset\u51fd\u6570\u4ea7\u751f\u7684\u7ed3\u6784\u4f53\uff0c\u7528\u4e8e\u5bf9\u4f18\u5316\u53c2\u6570\u7684\u8bbe\u7f6e\uff0c\u53ef\u4ee5\u7701\u7565\uff08\u91c7\u7528\u9ed8\u8ba4\u503c\uff09\u3002
Fsolve\u53ef\u4ee5\u6c42\u89e3\u7b80\u5355\u7684\u4e00\u7ef4\u975e\u7ebf\u6027\u65b9\u7a0b\uff0c\u5982\uff1a
x = fsolve(@myfun,[0.5 2 4],optimset('Display','iter')); %\u6c42\u89e3\u5728\u521d\u503c\u5206\u522b\u4e3a0.5\uff0c2\u548c4\u65f6\u65b9\u7a0b\u7684\u89e3
\u5176\u4e2d\uff0c\u51fd\u6570myfun\u7684\u5b9a\u4e49\u4e3a\uff1a
function F = myfun(x)
F = sin(x);
Fsolve\u8fd8\u53ef\u4ee5\u6c42\u89e3\u5927\u578b\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5982
x0 = [51.6;rand;unifrnd(-1,1);rand];
h=optimset;
h.MaxFunEvals=20000;
h.MaxIter=5000;
h.Display='off';
[p,fval] = fsolve(@f,x0,options);
\u6b64\u65f6\uff0c\u65b9\u7a0b\u7ec4\u53ef\u4ee5\u5199\u6210\u77e9\u9635\u5f62\u5f0f\uff1a
function F=f(x)
F=[x(1)+x(2)*(1-exp(-(x(3)*(0)^x(4))))-51.61;
x(1)+x(2)*(1-exp(-(x(3)*(9.78)^x(4))))-51.91;
x(1)+x(2)*(1-exp(-(x(3)*(30.68)^x(4))))-53.27;
x(1)+x(2)*(1-exp(-(x(3)*(59.7)^x(4))))-59.68;];
matlab\u4e2d\u89e3\u65b9\u7a0b\u7ec4\u8fd8\u662f\u5f88\u65b9\u4fbf\u7684\uff0c\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4ee3\u6570\u65b9\u7a0b\u7ec4Ax=b(A\u4e3a\u7cfb\u6570\u77e9\u9635\uff0c\u975e\u5947\u5f02)\u7684\u6c42\u89e3\uff0cMATLAB\u4e2d\u6709\u4e24\u79cd\u65b9\u6cd5\uff1a
(1)x=inv(A)*b \u2014 \u91c7\u7528\u6c42\u9006\u8fd0\u7b97\u89e3\u65b9\u7a0b\u7ec4\uff1b
(2)x=A\B \u2014 \u91c7\u7528\u5de6\u9664\u8fd0\u7b97\u89e3\u65b9\u7a0b\u7ec4
PS\uff1a\u4f7f\u7528\u5de6\u9664\u7684\u8fd0\u7b97\u6548\u7387\u8981\u6bd4\u6c42\u9006\u77e9\u9635\u7684\u6548\u7387\u9ad8\u5f88\u591a~
\u4f8b:
x1+2x2=8
2x1+3x2=13
>>A=[1,2;2,3];b=[8;13];
>>x=inv(A)*b
x =
2.00
3.00
>>x=A\B
x =
2.00
3.00\uff1b
\u5373\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3x1\u548cx2\u5206\u522b\u662f2\u548c3\u3002
\u5bf9\u4e8e\u540c\u5b66\u95ee\u5230\u7684\u7528matlab\u89e3\u591a\u6b21\u7684\u65b9\u7a0b\u7ec4\uff0c\u6709\u7b26\u53f7\u89e3\u6cd5\uff0c\u65b9\u6cd5\u662f\uff1a\u5148\u89e3\u51fa\u7b26\u53f7\u89e3,\u7136\u540e\u7528vpa(F,n)\u6c42\u51fan\u4f4d\u6709\u6548\u6570\u5b57\u7684\u6570\u503c\u89e3.\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a
\u7b2c\u4e00\u6b65:\u5b9a\u4e49\u53d8\u91cfsyms x y z ...;
\u7b2c\u4e8c\u6b65:\u6c42\u89e3[x,y,z,...]=solve('eqn1','eqn2',...,'eqnN','var1','var2',...'varN');
\u7b2c\u4e09\u6b65:\u6c42\u51fan\u4f4d\u6709\u6548\u6570\u5b57\u7684\u6570\u503c\u89e3x=vpa(x,n);y=vpa(y,n);z=vpa(z,n);...\u3002
\u5982\uff1a\u89e3\u4e8c\uff08\u591a\uff09\u5143\u4e8c\uff08\u9ad8\uff09\u6b21\u65b9\u7a0b\u7ec4\uff1a
x^2+3*y+1=0
y^2+4*x+1=0
\u89e3\u6cd5\u5982\u4e0b\uff1a
>>syms x y;
>>[x,y]=solve('x^2+3*y+1=0','y^2+4*x+1=0');
>>x=vpa(x,4);
>>y=vpa(y,4);
\u7ed3\u679c\u662f\uff1a
x =
1.635+3.029*i
1.635-3.029*i
-.283
-2.987
y =
1.834-3.301*i
1.834+3.301*i
-.3600
-3.307\u3002
\u4e8c\u5143\u4e8c\u6b21\u65b9\u7a0b\u7ec4\uff0c\u51714\u4e2a\u5b9e\u6570\u6839\uff1b
\u89e3\u7b54\u5982\u4e0b\uff1a
\u57fa\u672c\u65b9\u6cd5\u662f\uff1asolve(s1,s2,\u2026,sn,v1,v2,\u2026,vn)\uff0c\u5373\u6c42\u8868\u8fbe\u5f0fs1,s2,\u2026,sn\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff0c\u6c42\u89e3\u53d8\u91cf\u5206\u522bv1,v2,\u2026,vn\u3002
\u5177\u4f53\u4f8b\u5b50\u5982\u4e0b\uff1a
x^2 + x*y + y = 3
x^2 - 4*x + 3 = 0
\u89e3\u6cd5\uff1a
>> [x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0')
\u8fd0\u884c\u7ed3\u679c\u4e3a
x =
1 3
y =
1 -3/2
\u5373x\u7b49\u4e8e1\u548c3\uff1by\u7b49\u4e8e1\u548c-1.5
\u6216
>>[x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3= 0','x','y')
x =
1 3
y =
1 -3/2
\u7ed3\u679c\u4e00\u6837\uff0c\u4e8c\u5143\u4e8c\u65b9\u7a0b\u90fd\u662f4\u4e2a\u5b9e\u6839\u3002
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2\u3001\u53d8\u53c2\u6570\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3
\u5bf9\u4e8e\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u4e00\u822c\u7528fsolve\u547d\u4ee4\u5c31\u53ef\u4ee5\u4e86\uff0c\u4f46\u662f\u5bf9\u4e8e\u65b9\u7a0b\u7ec4\u4e2d\u67d0\u4e00\u7cfb\u6570\u662f\u53d8\u5316\u7684\uff0c\u8be5\u600e\u4e48\u6c42\u5462\uff1f
%\u5b9a\u4e49\u65b9\u7a0b\u7ec4\u5982\u4e0b\uff0c\u5176\u4e2dk\u4e3a\u53d8\u91cf
function F = myfun(x,k)
H=0.32;
Pc0=0.23;W=0.18;
F=[Pc0+H*(1+1.5*(x(1)/W-1)-0.5*(x(1)/W-1)^3)-x(2);
x(1)-k*sqrt(x(2))];
%\u6c42\u89e3\u8fc7\u7a0b
H=0.32;
Pc0=0.23;W=0.18;
x0 = [2*W; Pc0+2*H]; % \u53d6\u521d\u503c
options = optimset('Display','off');
k=0:0.01:1; % \u53d8\u91cf\u53d6\u503c\u8303\u56f4[0 1]
for i=1:1:length(k)
kk=k(i);
x = fsolve(@(x) myfun(x,kk), x0, options);%\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4
x1(i)=x(1);
x2(i)=x(2);
end
plot(k,x1,'-b',k,x2,'-r');
xlabel('k')
legend('x1','x2')
X=fsolve(@(X) hanshu(X),X0);
绛旓細fsolve鍑芥暟鐨勫父鐢ㄦ牸寮忥細[x,fval] = fsolve(fun,x0)渚嬪锛氳嚜瀹氫箟鏂圭▼缁勬枃浠 root2d.m function F = root2d(x)F(1) = exp(-exp(-(x(1)+x(2))) - x(2)*(1+x(1)^2);F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5;>>fun = @root2d;>>x0 = [0,0];...
绛旓細涓嶅ぇ娓呮浣犺姹傝В鐨勫叿浣撶殑鍑芥暟鏄粈涔堬紝浣嗕竴鑸潵璇fsolve鐨勭敤娉曞涓 1.鍏堝垱寤轰竴涓嚱鏁帮紝姣斿 function F = numel(x)F = [2*x(1)- x(2)- exp(-x(1));-x(1)+ 2*x(2)- exp(-x(2))];2.鍦ㄤ富鏂囦欢涓娇鐢╢solve鍑芥暟姹傝Вnumel(x)=0鐨勮В锛屽崟閫氬父浼氱粰涓涓垵濮嬪硷紝姣斿 x0 = [-5;...
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绛旓細鍒嗘瀽浜嗛涓荤殑涓夊厓涓娆℃柟绋嬬粍锛屽彲浠ョ敤vpasolve锛堬級鍑芥暟姹傝В锛岃鐢╢solve锛堬級鏉ユ眰瑙ｏ紝闇瑕佹壘鍒発0锛宬1锛宬2闄勮繎鍊硷紝鍚﹀垯鍙兘寰楀埌鐨勭粨鏋滃苟涓嶆槸浣犳兂瑕佺殑缁撴灉銆傝涓夊厓涓娆℃柟绋嬬粍姹傝В杩囩▼濡備笅锛歮=1660;t=[14.34 17.43 21.49];delta_c=[1.04 1.05 1.05];V0=[34.72 30.56 26.39];V1=[29.17...
绛旓細缁欎綘涓涓緥瀛愯鏄濡備綍浣跨敤fsolve鍑芥暟瑙ｉ潪绾挎ф柟绋嬬粍 鈶犲湪褰撳墠鐩綍锛屽缓绔嬪苟淇濆瓨fun.m鏂囦欢 function f= fun(x)f(1)=4*x(1)-x(2)+exp(x(1))/10-1 f(2)=-x(1)+4*x(2)+x(1)^2/8 鈶″湪褰撳墠鐩綍鍛戒护绐楀彛涓紝杈撳叆 x=fsolve(fun,[0锛0])...
绛旓細浠ヤ竴涓畝鍗曠殑涓轰緥a=8锛宐=7锛宑=6鏃 function F=fun(x)F=[sqrt(x(1)^2+x(2)^2)-8;sqrt(x(2)^2+x(3)^2)-7;sqrt(x(1)^2+x(3)^2)-6];淇濆瓨 璋冪敤x0=[0;0;0];[x,fv]=fsolve('fun',x0)x0鏄垵濮嬪间换鎰忕殑 鍛戒护fsolve锛坒锛寈0锛夌殑鎰忔濇槸浠巟0寮濮嬫悳浣垮緱f=0鐨勮В 寰...
绛旓細function [q,p,t]=syfsolves ii=0;q=zeros(1,100);p=zeros(1,100);t=zeros(1,100);for a=1:100 bi=num2str(a);b=[bi,'*x^2-8*x+cos(x)'];ii=ii+1;[q(ii),p(ii),t(ii)]=fsolve(b,rand(1));end end 鍏朵腑q浠ｈ〃浣挎柟绋嬬殑瑙 p浠ｈ〃鍦ㄦ柟绋嬪彇q鐨勫 t浠ｈ〃鍋滄姹傝В鐨勫師鍥...
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绛旓細clear all;clc;close all;fzero('(x.^7)+2*(x.^5)+1',0)
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