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math.RA2009★ 31 cited
CSR expansions of matrix powers in max algebra
Sergei Sergeev, Hans Schneider
We study the behavior of max-algebraic powers of a reducible nonnegative n by n matrix A. We show that for t>3n^2, the powers A^t can be expanded in max-algebraic powers of the for…
math.MG2009★ 3 cited
On hyperplanes and semispaces in max-min convex geometry
Viorel Nitica, Sergei Sergeev
The concept of separation by hyperplanes is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry a…
math.RA2009★ 3 cited
Cyclic classes and attraction cones in max algebra
Sergei Sergeev
In max algebra it is well-known that the sequence A^k, with A an irreducible square matrix, becomes periodic at sufficiently large k. This raises a number of questions on the perio…