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We introduce the class of skew-circulant lattice rules. These are s-dimensional lattice rules that may be generated by the rows of an s × s skew-circulant matrix. (This is a minor variant of the familiar circulant matrix.) We present briefly some of the underlying theory of these matrices and rules. We are particularly interested in finding rules of(More)
Many problems have multiple layers of parallelism. The outer-level may consist of few and coarse-grained tasks. Next, each of these tasks may also be rich in parallelism, and be split into a number of fine-grained tasks, which again may consist of even finer subtasks, and so on. Here we argue and demonstrate by examples that utilizing multiple layers of(More)
The problem of partitioning a sequence of n real numbers into p intervals is considered. The goal is to nd a partition such that the cost of the most expensive interval measured with a cost function f is minimized. An eecient algorithm which solves the problem in time O(p(n ? p) log p) is developed. The algorithm is based on nding a sequence of feasible(More)
In this paper we discuss the use of nested parallelism. Our claim is that if the problem naturally possesses multiple levels of parallelism, then applying parallelism to all levels may significantly enhance the scalability of your algorithm. This claim is sustained by numerical experiments. We also discuss how to implement multi-level parallelism using(More)
In this paper we describe some of the salient features of our search program for finding good lattices. The reciprocals of these lattices are used in lattice integration rules, of which number theoretic rules form a major subset. We describe algorithms for ϱ(⋎), the Zaremba index (or figure of merit) of an integer lattice ⋎. We describe a search algorithm(More)
In this paper we report on the parallelization of a split-step algorithm for the Schrödinger equation. The problem is represented in spherical coordinates in physical space and transformed to Fourier space for operation by the Laplacian operator, and Legendre space for operation by the Angular momentum operator and the Potential operator. Timing results are(More)
In this paper we describe how to apply ne grain parallelism to augmenting path algorithms for the dense linear assignment problem. We prove by doing that the technique we suggest, can be eeciently implemented on commercial available, massively parallel computers. Using n processors, our method reduces the computational complexity from the sequential O(n 3)(More)