matlab怎么计算方程组 matlab 求助 解方程组
\u600e\u4e48\u7528matlab\u89e3\u542b\u6709\u5b57\u6bcd\u7cfb\u6570\u7684\u65b9\u7a0b\u7ec4\u7684\u89e3\uff0c\u4e3e\u4e2a\u7b80\u5355\u4f8b\u5b50\u7528\u6cd5\u4ee5\u8fd9\u4e2a\u4e3a\u4f8b\uff1a
x+A*y=10
x-B*y=1
\u5176\u4e2dx,y\u4e3a\u53d8\u91cf,A,B\u4e3a\u5b57\u6bcd\u7cfb\u6570.
\u53ea\u8981\u5728Matlab\u4e2d\u8f93\u5165
syms x,y,A,B
[x y]=solve('x+A*y=10','x-B*y=1','x','y')
\u5373\u53ef\u6c42\u51fa\u89e3
x =
(A + 10*B)/(A + B)
y =
9/(A + B)
\u5bf9\u4e8e\u51fd\u6570solve\u7684\u5177\u4f53\u7528\u6cd5,\u53ef\u4ee5\u901a\u8fc7\u8f93\u5165help solve\u6765\u5b66\u4e60\u3002
\u6269\u5c55\u8d44\u6599\uff1amatlab\u4e2d\u65b9\u7a0b\u6c42\u89e3\u7684\u57fa\u672c\u547d\u4ee4
1.roots(p) %\u6c42\u591a\u9879\u5f0f\u7684\u6839\uff0c\u5176\u4e2dp\u662f\u591a\u9879\u5f0f\u5411\u91cf\u3002
\u4f8b\u6c42x3-x2+x-1=0\u7684\u6839
\u89e3\uff1a>>roots([1,-1,1,-1])
\u6ce8\uff1a [1,-1,1,-1]\u5728matlab\u4e2d\u8868\u793a\u591a\u9879\u5f0f x3-x2+x-1
2.solve(fun) %\u6c42\u65b9\u7a0bfun=0\u7684\u7b26\u53f7\u89e3\uff0c\u5982\u679c\u4e0d\u80fd\u6c42\u5f97\u7cbe\u786e\u7684\u7b26\u53f7\u89e3\uff0c\u53ef\u4ee5\u8ba1\u7b97\u53ef\u53d8\u7cbe\u5ea6\u7684\u6570\u503c\u89e3
\u4f8b\uff1a\u7528solve\u6c42\u65b9\u7a0bx9+x8+1=0\u7684\u6839
\u89e3\uff1a>>solve(\u2018x^9+x^8+1\u2019)
\u7ed9\u51fa\u4e86\u65b9\u7a0b\u7684\u6570\u503c\u89e3\uff0832\u4f4d\u6709\u6548\u6570\u5b57\u7684\u7b26\u53f7\u91cf\uff09
3.solve(fun,var) %\u5bf9\u6307\u5b9a\u53d8\u91cfvar\u6c42\u4ee3\u6570\u65b9\u7a0bfun=0\u7684\u7b26\u53f7\u89e3\u3002
\u4f8b\uff1a\u89e3\u65b9\u7a0b ax2+bx2+c=0
\u89e3\uff1a>>syms a b c x;
>>f=a*x^2+b*x+c;
>>solve(f)
\u5982\u679c\u4e0d\u6307\u660e\u53d8\u91cf\uff0c\u7cfb\u7edf\u9ed8\u8ba4\u4e3ax,\u4e5f\u53ef\u6307\u5b9a\u81ea\u53d8\u91cf\uff0c\u6bd4\u5982\u6307\u5b9ab\u4e3a\u81ea\u53d8\u91cf
>>symsa b c x;
>> f=a*x^2+b*x+c;
>>solve(f,b)
4.fsolve(fun,x0) %\u6c42\u975e\u7ebf\u6027\u65b9\u7a0bfun=0\u5728\u4f30\u8ba1\u503cx0\u9644\u8fd1\u7684\u8fd1\u4f3c\u89e3\u3002
\u4f8b\uff1a\u7528fsolve\u6c42\u65b9\u7a0bx=e-x\u57280\u9644\u8fd1\u7684\u6839
\u89e3\uff1a>>fsolve(\u2018x-exp(-x)\u2019,0)
5.fzero(fun,x0) %\u6c42\u51fd\u6570fun\u5728x0\u9644\u8fd1\u7684\u96f6\u70b9
\u4f8b\uff1a\u6c42\u65b9\u7a0bx-10x+2=0\u5728x0=0.5\u9644\u8fd1\u7684\u6839
\u89e3\uff1a>>fzero(\u2018x-10^x+2\u2019,0.5)
\u4e00\u3002\u7528matlab \u4e2d\u7684solve\u51fd\u6570
>>syms x y; %\u5b9a\u4e49\u4e24\u4e2a\u7b26\u53f7\u53d8\u91cf\uff1b
>>[x ,y]=solve('y=2*x+3','y=3*x-7');%\u5b9a\u4e49\u4e00\u4e2a 2x1 \u7684\u6570\u7ec4\uff0c\u5b58\u653ex\uff0cy
>>x
>>x=10.0000
>>y
>>y=23.0000
\u4e8c\u3002\u7528matlab \u4e2d\u7684\u53cd\u5411\u659c\u7ebf\u8fd0\u7b97\u7b26\uff08backward slash\uff09
\u5206\u6790\uff1a
\u65b9\u7a0b\u7ec4\u53ef\u5316\u4e3a
2*x-y=-3\uff1b
3*x-y=7\uff1b
AX=B (*)
A=[2,-1;3,-1]; B=[-3,7];
X=A\B %\u53ef\u4ee5\u770b\u6210\u5c06\uff08*\uff09\u5f0f\u5de6\u8fb9\u90fd\u9664\u4ee5\u7cfb\u6570\u77e9\u9635A
>>A=[2,-1;3,-1];
>>B=[-3,7];
>>X=A\b
X =
10.0000 % x = 10.0000
23.0000 % y = 23.0000
1、对于比较简单的方程组，可以用solve（）函数命令求解。如方程组 x + y = 1 ； x - 11y = 5
>>[x,y]=solve('x + y = 1','x - 11*y = 5')
又如方程组 exp(x+1)-y²=10 ；ln(x)+3y=7
>>syms x y
>>[x,y]=solve(exp(x+1)-y^2-10,log(x)+3*y-7,'x','y')
2、对于比较复杂的方程组，可以用数值方法中的牛顿迭代法，二分法来求解。如方程组
求解代码
x0=[1.0 1.0 1.0]';
tol = 1.0e-6;
x = x0 - newton_dfun(x0)
ewton_fun(x0); %newton_dfun导函数，newton_fun函数
n = 1;
while (norm(x-x0)>tol) && (n<1000)
x0 = x;
x = x0 - newton_dfun(x0)
ewton_fun(x0);
n = n + 1;
end
x
求解结果为
x = 0.69829；y = 0.62852；z= 0.34256
matlab中解方程组还是很方便的，例如，对于代数方程组Ax=b(A为系数矩阵，非奇异)的求解，MATLAB中有两种方法：
(1)x=inv(A)*b — 采用求逆运算解方程组；
(2)x=A\B — 采用左除运算解方程组
PS：使用左除的运算效率要比求逆矩阵的效率高很多~
例:
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；
即二元一次方程组的解x1和x2分别是2和3。
对于同学问到的用matlab解多次的方程组，有符号解法，方法是：先解出符号解,然后用vpa(F,n)求出n位有效数字的数值解.具体步骤如下：
syms x1 x2 x3 x4 x5 f1 f2 f3 f4 f5
f1=(x1+x2+x3+x4+x5+22.55*x1*x4+7.63*x3*x4+148.222*x1^3*x4+5.86*10^13*x1^12*x4^7+67.03*x1*x4^2+212.17*x1*x4^6+338.08*x1*x5+4948932.908*x1^3*x5^2+3522485477*x1^4*x5^3+3.46*x4*x5+4.109*x3*x5+6.03*x3*x5^2+4.847*x3^2*x5+135498.74*x1^3*x2*x4^3+7.55*10^14*x1^11*x2*x4^7)-1;
f2=0.5653*(1/3*x2+135498.74*x1^3*x2*x4^3+7.55*10^14*x1^11*x2*x4^7)-0.2946*(0.5*x1+22.55*x1*x4+444.666*x1^3*x4+7.03*10^14*x1^12*x4^7+67.03*x1*x4^2+212.17*x1*x4^6+338.08*x1*x5+14846798.72*x1^3*x5^2+1.41*10^10*x1^4*x5^3+406496.24*x1^3*x2*x4^3+8.305*10^15*x1^11*x2*x4^7);
f3=0.2946*(0.5*x3+7.63*x3*x4+4.109*x3*x5+6.03*x3*x5^2+9.694*x3^2*x5)-0.05*(1/3*x2+135498.74*x1^3*x2*x4^3+7.55*10^14*x1^11*x2*x4^7);
f4=0.05*(x4+22.55*x1*x4+7.63*x3*x4+148.222*x1^3*x4+4.102*10^14*x1^12*x4^7+134.06*x1*x4^2+1273.02*x1*x4^6+3.46*x4*x5+406496.24*x1^3*x2*x4^3+5.285*10^15*x1^11*x2*x4^7)-0.3456*(0.5*x3+7.63*x3*x4+4.109*x3*x5+6.03*x3*x5^2+9.694*x3^2*x5);
f5=0.3456*(x5+338.08*x1*x5+9897865.816*x1^3*x5^2+1.056*10^10*x1^4*x5^3+3.46*x4*x5+4.109*x3*x5+12.06*x3*x5^2+4.847*x3^2*x5)-0.05*(x4+22.55*x1*x4+7.63*x3*x4+148.222*x1^3*x4+4.102*10^14*x1^12*x4^7+134.06*x1*x4^2+1273.02*x1*x4^6+3.46*x4*x5+406496.24*x1^3*x2*x4^3+5.285*10^15*x1^11*x2*x4^7);
[solx1 solx2 solx3 solx4 solx5]=solve(f1==0,f2==0,f3==0,f4==0,f5==0,x1,x2,x3,x4,x5);
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绛旓細Matlab鍙互浣跨敤鈥淺鈥濆嚱鏁版眰瑙ｇ嚎鎬鏂圭▼缁鐨勮В銆1. 浣跨敤鈥淺鈥濆嚱鏁 浣跨敤鈥淺鈥濆嚱鏁板彲浠ユ眰瑙ｅ舰濡侫x=b鐨勭嚎鎬ф柟绋嬬粍锛屽叾涓瑼鏄郴鏁扮煩闃碉紝b鏄父鏁板悜閲忋備緥濡傦紝瑕佹眰瑙ｅ涓嬬嚎鎬ф柟绋嬬粍锛3x + 2y = 7 4x - 5y = -8 鍒欏彲浠ユ寜鐓т互涓嬫楠よ繘琛岋細```matlab 瀹氫箟绯绘暟鐭╅樀A鍜屽父鏁板悜閲廱 A = [3, 2; 4, -5]...
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绛旓細棰樹富缁欏嚭鐨勫鏉傜殑鍒嗗紡鏂圭▼缁锛屽彲浠ョ敤vpasolve锛堬級鍑芥暟寰楀埌鍏舵暟鍊艰В銆傛眰瑙ｆ柟娉曞涓:syms x y eq1=x-(107.1+0.2*(4*y+3*x)*(3.83-107.1)/(4*y+3*3.83));eq2=y-(83.7+y*(4*y+3*x)*(1.28-83.7)/(3*x*(3*y+2*1.28)+4*y*(2*y+3*1.28)));[x,y]=vpasolve...
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