The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles shared-memory style programming with e cient exploitation of data locality. The BSPRAM model can be optimally si...

A key technique for controlling numerical stability in sparse direct solvers is threshold partial pivoting. When selecting a pivot, the entire candidate pivot column below the diagonal must be up-to-date and must be scanned. If the factorization is parallelized across a large number of cores, communication latencies can be the dominant computational cost. In this paper, we propose two alternati...

One way, how to speed up the computation of the singular value decomposition of a given matrix A ∈ Cm×n, m ≥ n, by the parallel two-sided block-Jacobi method, consists of applying some pre-processing steps that would concentrate the Frobenius norm near the diagonal. Such a concentration should hopefully lead to fewer outer parallel iteration steps needed for the convergence of the entire algori...

In Data Envelopment Analysis (DEA), identification of the Pareto-efficient frontier of an empirical production possibility set is a prerequisite step toward determining rates of change of outputs with changes in inputs along its piecewise linear facets. These rates of change, which will be different on different facets, have important economic and managerial implications in trade-off analysis, ...

The traditional perturbution (or lexicographic) methods for resolving degeneracy in linear programming impose decision rules that eliminate ties in the simplex ratio rule and, therefore, restrict the choice of exiting basic variables. Bland's combinatorial pivoting rule also restricts the choice of exiting variables. Using ideas from parametric linear programming, we develop anti-cycling pivoti...

This paper presents a pivoting-based method for solving convex quadratic programming and then shows how to use it together with a parameter technique to solve mean-variance portfolio selection problems.

A signiicant collection of two-point boundary value problems is shown to give rise to linear systems of algebraic equations on which Gaussian elimination with row partial pivoting is unstable when standard solution techniques are used.