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An equivalent matrix pencilfor bivariate polynomial matrices

Mohamed Boudellioua (2006)

International Journal of Applied Mathematics and Computer Science

In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.

An idempotent algorithm for a class of network-disruption games

William M. McEneaney, Amit Pandey (2016)

Kybernetika

A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even...

An improvement of an inequality of Fiedler leading to a new conjecture on nonnegative matrices

Assaf Goldberger, Neumann, Michael (2004)

Czechoslovak Mathematical Journal

Suppose that A is an n × n nonnegative matrix whose eigenvalues are λ = ρ ( A ) , λ 2 , ... , λ n . Fiedler and others have shown that det ( λ I - A ) ≤ λ n - ρ n , for all λ > ρ , with equality for any such λ if and only if A is the simple cycle matrix. Let a i be the signed sum of the determinants of the principal submatrices of A of order i × i , i = 1 , ... , n - 1 . We use similar techniques to Fiedler to show that Fiedler’s inequality can be strengthened to: det ( λ I - A ) + ∑ i = 1 n - 1 ρ n - 2 i | a i | ( λ - ρ ) i ≤ λ n - ρ n , for all λ ≥ ρ . We use this inequality to derive the inequality that: ∏ 2 n ( ρ - λ i ) ≤ ρ n - 2 ∑ i = 2 n ( ρ - λ i ) . In the spirit of a celebrated conjecture due to Boyle-Handelman,...

Currently displaying 321 – 340 of 396