Showing papers on "Parallel algorithm published in 1973"
TL;DR: This paper uses a technique called recursive doubling in an algorithm for solving a large class of recurrence problems on parallel computers such as the Iliac IV.
Abstract: An mth-order recurrence problem is defined as the computation of the series x 1 , x 2 , ..., X N , where x i = f i (x i-1 , ..., x i-m ) for some function f i . This paper uses a technique called recursive doubling in an algorithm for solving a large class of recurrence problems on parallel computers such as the Iliac IV. Recursive doubling involves the splitting of the computation of a function into two equally complex subfunctions whose evaluation can be performed simultaneously in two separate processors. Successive splitting of each of these subfunctions spreads the computation over more processors. This algorithm can be applied to any recurrence equation of the form x i = f(b i , g(a i , x i-1 )) where f and g are functions that satisfy certain distributive and associative-like properties. Although this recurrence is first order, all linear mth-order recurrence equations can be cast into this form. Suitable applications include linear recurrence equations, polynomial evaluation, several nonlinear problems, the determination of the maximum or minimum of N numbers, and the solution of tridiagonal linear equations. The resulting algorithm computes the entire series x 1 , ..., x N in time proportional to [log 2 N] on a computer with N-fold parallelism. On a serial computer, computation time is proportional to N.
1,264 citations
TL;DR: An efficient parallel algorithm is presented in which computation time grows as log 2, which can be used to solve recurrence relations of all orders.
Abstract: Tridiagonal linear systems of equations can be solved on conventional serial machines in a time proportional to N, where N is the number of equations The conventional algorithms do not lend themselves directly to parallel computation on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial An efficient parallel algorithm is presented in which computation time grows as log2N The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders
318 citations
TL;DR: The computational theory of dynamic programming is examined from the viewpoint of parallel computation and parallel aspects of various dimensionality reduction techniques such as state increment dynamic programming, successive approximations, and shift vectors are given.
Abstract: The computational theory of dynamic programming is examined from the viewpoint of parallel computation. A discussion of various forms of parallelism, the corresponding parallel algorithms, the applicability of the algorithms to different types of optimization problems, and their advantages over serial computation is presented. In addition, parallel aspects of various dimensionality reduction techniques such as state increment dynamic programming, successive approximations, and shift vectors are also given.
46 citations
01 Dec 1973
TL;DR: In this paper, a parallel variable metric algorithm was proposed to exploit parallel computing or vector streaming (pipeline) capabilities of computers, and the convergence of the iterates to the solution was proved for a quadratic functional on a real separable Hilbert space.
Abstract: An algorithm, designed to exploit the parallel computing or vector streaming (pipeline) capabilities of computers is presented. When p is the degree of parallelism, then one cycle of the parallel variable metric algorithm is defined as follows: first, the function and its gradient are computed in parallel at p different values of the independent variable; then the metric is modified by p rank-one corrections; and finally, a single univariant minimization is carried out in the Newton-like direction. Several properties of this algorithm are established. The convergence of the iterates to the solution is proved for a quadratic functional on a real separable Hilbert space. For a finite-dimensional space the convergence is in one cycle when p equals the dimension of the space. Results of numerical experiments indicate that the new algorithm will exploit parallel or pipeline computing capabilities to effect faster convergence than serial techniques.
37 citations
TL;DR: The recent development of parallel processing algorithms for solving optimal control problems for nonlinear dynamic systems, both the deterministic and stochastic cases are considered.
Abstract: This paper describes the recent development of parallel processing algorithms for solving optimal control problems for nonlinear dynamic systems. Both the deterministic and stochastic cases are considered. The resulting algorithms are applicable to a large range of parallel architecture computers, including Iliac IV, associative processors, and potential designs based on integrated circuit technology.
25 citations
Proceedings Article•
01 Jan 197314 citations
TL;DR: The algorithm is structured in a way which enables many of the operations to be performed in parallel; the parallelisms in the algorithm have had an impact on the conceptual design of an array computer.
8 citations
TL;DR: A computational algorithm is developed for a parallel processing computer using the inviscid compressible supercritical flow over a circular cylinder as an example and all boundary conditions are satisfied explicitly and boundary points are computed in parallel with interior points, thereby greatly increasing the “machine utilization.”
4 citations