Max-plus algebra eigenvalue and eigenvector
[l,v,d] = maxplusmaxalgolpoly(A)
: a positve integer number that represents the period of vectors
x(q),x(q+1),⋯,x(p-1),x(p), where d = p-q and x(p) = l⊗x(q).
The function valid for both an irreducible and a reducible matrix A as long as the cycle time vector of matrix A contains all elements equal to the same constant, and returns eigenvector and a unique corresponding eigenvalue of matrix A. If the condition is not satisfied the function returns error. And if numerical error this function maxplusmaxalgol still work but A⊗v≠l⊗v and the norm of A⊗v - l⊗v given by norm(A⊗x - l⊗v)≤4.019D-14 .
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.
If the matrix A irreducible, instead of use function maxalgol, the time computation will more faster.
A=maxpluszeros(6,6); A(:,:,2) =[-%inf 3. -%inf -%inf 7. -%inf; 2. -%inf 6. -%inf 7. 2.; -%inf 7. 8. 9. -%inf -%inf; -%inf -%inf -%inf 1. 2. -%inf; 8. -%inf 7. -%inf -%inf 2.; 0. -%inf -%inf 6. 5. -%inf]; [l,v,d] = maxplusmaxalgolpoly(A) | ![]() | ![]() |