97 citations · 431 across the 34 of their papers we have counts for
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The level set method for the two-sided eigenproblem
Stephane Gaubert, Sergei Sergeev
We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a f…
On commuting matrices in max algebra and in classical nonnegative algebra
Ricardo D. Katz, Hans Schneider, Sergei Sergeev
This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analog…
Basic solutions of systems with two max-linear inequalities
Sergei Sergeev, Edouard Wagneur
We give an explicit description of the basic solutions of max-linear systems with two inequalities.
On the problem Ax=λBx in max algebra: every system of intervals is a spectrum
Sergei Sergeev
We consider the two-sided eigenproblem Ax=λBx over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.