We propose new methods which combine aggregation with point and block iterative techniques for computing the stationary probability vector of a finite ergodic Markov chain. These techniques are also compared numerically with several methods which have recently appeared in the literature for the class of nearly completely decomposable Markov chains.

Iterative methods for computing stationary distributions of nearly completely decomposable markov chains

Scalar fields arise in every scientific application. Existing scalar visualization techniques require that the user infers the global scalar structure from what is frequently an insufficient display of information. We present a visualization technique which numerically detects the structure at all scales, removing from the user the responsibility of extracting information implicit in the data, and presenting the structure explicitly for analysis. We further demonstrate how scalar topology detection proves useful for correct visualization and image processing applications such as image co-registration, isocontouring, and mesh compression.

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Visualization of scalar topology for structural enhancement

A method for constructing shape-preserving surfaces interpolating arbitrary sets of data on rectangular grids is presented. The surfaces are tensor product splines of arbitrary continuity class which extend some properties of univariate shape-preserving splines given in earlier papers.

Shape-preserving bivariate interpolation

Equivalence and decomposition in queueing systems—A unified approach

The purpose of this paper is to report on a comparison of an implementation of a simple direct $LU$ factorization method, suggested by Funderlic and Mankin [SIAM J. Sci. Stat. Comput., 2 (1981), pp. 375–383], with other direct methods recommended by Paige, Styan and Wachter [J. Stat. Comput.Simul., 4 (1975), pp. 173–186], for computing stationary distributions of Markov chains. A backward error analysis is developed and conditioning problems are addressed. The method is stable without pivoting, it is numerically efficient and it lends itself to symmetric pivoting to preserve sparsity.

Comparison of Some Direct Methods for Computing Stationary Distributions of Markov Chains

Compared with other methods, this technique for smooth surface interpolation over grid data reduces the number of extraneous local optima and inflection points of the surface.

S. L. Dodd

Papers

Shape-Preserving Spline Interpolation for Specifying Bivariate Functions on Grids

An Iterative Method for the Exact Solution of Coxian Queueing Networks.