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Start Over Author "Dendievel, Sarah" Publisher society for industrial & applied mathematics
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1. GENERAL SOLUTION OF THE POISSON EQUATION FOR QUASI-BIRTH-AND-DEATH PROCESSES.

Author

BINI, DARIO, DENDIEVEL, SARAH, LATOUCHE, GUY, and MEINI, BEATRICE

Subjects
*NUMERICAL solutions to Poisson's equation, *TOEPLITZ matrices, *NUMERICAL solutions to difference equations, *RESOLVENTS (Mathematics), *INFINITY (Mathematics)
Abstract

We consider the Poisson equation (I -- P)u = g, where P is the transition matrix of a quasi-birth-and-death process with infinitely many levels, g is a given infinite dimensional vector, and u is the unknown. Our main result is to provide the general solution of this equation. To this purpose we use the block tridiagonal and block Toeplitz structure of the matrix P to obtain a set of matrix difference equations, which are solved by constructing suitable resolvent triples. [ABSTRACT FROM AUTHOR]

Published
2016
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