是否存在一种算法可以计算奇异矩阵的Drazin逆? 我想在MATLAB
或Mathematica
中应用它。
阅读本文:
Fanbin Bu 和 Yimin Wei,《计算双变量多项式矩阵Drazin逆的算法》,《应用数学和计算》147.3(2004):805-836。
附录中有几个MATLAB代码。第一个代码如下:
function DrazinInverse1a = DrazinInverse1(a)
%-----------------------------------------
%Compute the Drazin Inverse of a matrix 'a' using the limited algorithm.
%Need computing the index of 'a'.
global q1 q2 s1 s2
[m,n] = size(a);
if m~= n
disp('Matrix is must be square!')
end
%-----------------------------------------
% Computer the index of A and note r = rank(A^k).
[k,r,a1,a] = index(a);
F = eye(n);
g = -trace(a);
g = collect(g);
for i = 1:r-1
G = g*eye(n);
F = a*F+G;
g = -trace(a*F)/(i+1);
g = collect(g);
end
DrazinInverse1a = a1*F;
DrazinInverse1a = -1/g*DrazinInverse1a;
DrazinInverse1a = simplify(DrazinInverse1a);
end
function [k,r,a1,a] = index(a)
%To compute the index of 'a'.
k = 0;
n = length(a);
r = n;
a0 = a;
r1 = rank(a);
a1 = eye(n);
while r ~= r1
r = r1;
a1 = a;
a = a*a0;
r1 = rank(a);
k = k+1;
end
r = sym2poly(r);
end
Drazin逆
。 - thanasissdr