Diaconis, Persi; Neuberger, J. W. Numerical results for the Metropolis algorithm. (English) Zbl 1058.65010 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. Cited in 1 ReviewCited in 4 Documents 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 PDFBibTeX XMLCite \textit{P. Diaconis} and \textit{J. W. Neuberger}, Exp. Math. 13, No. 2, 207--213 (2004; Zbl 1058.65010) Full Text: DOI Euclid EuDML References: [1] Billera L., Stat. Sci. 20 pp 1– (2001) [2] DOI: 10.1006/jcss.1998.1576 · Zbl 0920.68054 · doi:10.1006/jcss.1998.1576 [3] Diaconis P., ”On the Spectrum of a Simple Metropolis Algorithm (2003) [4] Edmunds D. E., Spectral Theory and Differential Operators. (1987) · Zbl 0628.47017 [5] Kienetz J., PhD diss., in: ”Convergence of Markov Chains via Analytic and Isoperimetric Inequalities.” (2000) [6] DOI: 10.1142/S0218127496000680 · Zbl 0920.73165 · doi:10.1142/S0218127496000680 [7] DOI: 10.1214/aos/1033066201 · Zbl 0854.60065 · doi:10.1214/aos/1033066201 [8] DOI: 10.1063/1.1699114 · doi:10.1063/1.1699114 [9] DOI: 10.1007/BFb0103812 · doi:10.1007/BFb0103812 [10] DOI: 10.1002/jcc.540080425 · doi:10.1002/jcc.540080425 [11] Neuberger J. W., Exp. Math. 8 pp 301– (1999) [12] Sullivan F., Computing in Science and Engineering 2 (2000) [13] DOI: 10.1214/aos/1176325750 · Zbl 0829.62080 · doi:10.1214/aos/1176325750 [14] Wilkinson J. H., The Algebraic Eigenvalue Problem. (1965) · Zbl 0258.65037 [15] DOI: 10.1016/S0304-4149(99)00101-5 · Zbl 1045.60073 · doi:10.1016/S0304-4149(99)00101-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.