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Directed forests with application to algorithms related to Markov chains

Piotr Pokarowski (1999)

Applicationes Mathematicae

This paper is devoted to computational problems related to Markov chains (MC) on a finite state space. We present formulas and bounds for characteristics of MCs using directed forest expansions given by the Matrix Tree Theorem. These results are applied to analysis of direct methods for solving systems of linear equations, aggregation algorithms for nearly completely decomposable MCs and the Markov chain Monte Carlo procedures.

Epsilon-inflation with contractive interval functions

Günter Mayer (1998)

Applications of Mathematics

For contractive interval functions [ g ] we show that [ g ] ( [ x ] ϵ k 0 ) ⊆ ∫ ( [ x ] ϵ k 0 ) results from the iterative process [ x ] k + 1 : = [ g ] ( [ x ] ϵ k ) after finitely many iterations if one uses the epsilon-inflated vector [ x ] ϵ k as input for [ g ] instead of the original output vector [ x ] k . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

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