A Modified Arnoldi Iteration for Transition Probability Matrices of Reversible Markov Chains.

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2018-08
Authors
Chong, Joseph M. U.
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Electrical Engineering
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Reversible Markov chains are used for modeling many physical and network phenomena. The second largest eigenvalue magnitude of the transition probability matrix gives a upper bound on the mixing time of a reversible Markov chain, but is incalculable for large transition probability matrices using typical eigenvalue algorithms. We present the Modified Arnoldi iteration - a modification of the Arnoldi iteration for reversible Markov chains that utilizes sample estimates where matrix operations may be infeasible, thereby being a possible option when usual algorithms are nonviable.
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