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

Date: 2018-08-01 Add to Google CalendarTime: 12:00pm

Location: Holmes Hall 389

Speaker: Joseph Chong, EE MS Candidate

Abstract:

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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