怎么用MATLAB求解这个二次矩阵方程a0=[2 3;6 4];a1=[-10 1;-20 3];a2=[1 3;5 2];syms p1 p2 p3 p4 p; p=[p1 p2;p3 p4]; 二次矩阵方程是：p^2*a2+p*a1+a0;

Question

怎么用MATLAB求解这个二次矩阵方程
a0=[2 3;6 4];
a1=[-10 1;-20 3];
a2=[1 3;5 2];
syms p1 p2 p3 p4 p;
p=[p1 p2;p3 p4];
二次矩阵方程是：p^2*a2+p*a1+a0;

Answer 1

clear
a0=[2 3;6 4];
a1=[-10 1;-20 3];
a2=[1 3;5 2];
syms p1 p2 p3 p4 p;
p=[p1 p2;p3 p4]
%二次矩阵方程是：p^2*a2+p*a1+a0=0;
eq=p^2*a2+p*a1+a0;
[p1,p2,p3,p4]=solve(eq(1,1),eq(1,2),eq(2,1),eq(2,2),p1,p2,p3,p4);
p1=double(p1);p2=double(p2);p3=double(p3);p4=double(p4);
t=1;
[m,n]=size(p1);
pp=zeros(2,2,m);
for i=1:m
if (imag(p1(i))==0)&(imag(p2(i))==0)&(imag(p3(i))==0)&(imag(p4(i))==0)
P1=p1(i,1);P2=p2(i,1);P3=p3(i,1);P4=p4(i,1);
pp(:,:,t)=[P1,P2;P3,P4];
t=t+1;
end
end
pp=subs(pp);
P=pp(:,:,1:t-1)
p =
[ p1,p2]
[ p3,p4]
P(:,:,1) =
11.1677 -5.6672
21.7147 -10.9798
P(:,:,2) =
-3.5248 4.0911
-5.8176 6.2600
带回去验算：误差10^-13
P(:,:,1)^2*a2+P(:,:,1)*a1+a0
ans =
1.0e-013 *
0.1421 -0.0711
0.5684 -0.1776
>> P(:,:,2)^2*a2+P(:,:,2)*a1+a0
ans =
1.0e-013 *
0.0711 0.1243
0.2842 0.0178