Numerical results for the Metropolis algorithm. (English) Zbl 1058.65010

Diaconis, Persi; Neuberger, J. W.

Exp. Math. 13, No. 2, 207-213 (2004).

Summary: This paper deals with the spectrum of an operator associated with a special kind of random walk. The operator is related to the Metropolis algorithm, an important tool of large-scale scientific computing. The spectrum of this operator has both discrete and continuous parts. There is an interesting challenge due to the fact that any finite-dimensional approximation has only eigenvalues. Patterns are presented which give an idea of the full spectrum of this operator.

MSC:

65C40	Numerical analysis or methods applied to Markov chains
65C05	Monte Carlo methods
60J22	Computational methods in Markov chains
60G50	Sums of independent random variables; random walks
68W30	Symbolic computation and algebraic computation

Keywords:

numerical examples; computational Markov chain; spectrum; random walk; Metropolis algorithm; large-scale scientific computing; eigenvalues

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