Bipartite Min-Max-plus algebra eigenvalue and eigenvector
[eigval,eigvec] = minmaxpluspowalgol(A,B)
Bipartite min-max-plus system given by equations
x(+1) = A⊗y(k) and y(k) = B⊗' x(k) for k = 0,1,2,⋯ (1)
where A∊ℝεn×m, B ∊ℝT m×n, x(k)∊ℝεn, and y(k) ∊ℝT m
The equation (1) can be written as a simple notation that is given by :
z(k+1) = ℳ(z(k)) ....(2)
where z(k)=(x(k),y(k))t, ℳ((x(k),y(k))t )=(A⊗y(k),B⊗'x(k))t .
The function returns eigenvector and an unique corresponding eigenvalue of matrix ℳ=(A,B) of size n∔m . According to the reference below, assumption of the function, the periodic behaviour of bipartite of min-max-plus system (1) is constant.
For details see: Subiono and J.van der Woude (2000); "Power algorithms for (max,∔)- and bipartite (min,max,∔)-systems"; DEDS, vol.10, pp.369-389, 2000.