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

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
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