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Tuesday, July 28, 2020 | History

2 edition of parallel triangular solver for a hypercube multiprocessor found in the catalog.

parallel triangular solver for a hypercube multiprocessor

Guangye Li

parallel triangular solver for a hypercube multiprocessor

by Guangye Li

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Published by Cornell Theory Center, Cornell University in Ithaca, N.Y .
Written in English


Edition Notes

StatementGuangye Li, Thomas F.Coleman.
SeriesTechnical report / Cornell Theory Center -- CTC86TR8., Technical report (Cornell Theory Center) -- 8.
ContributionsColeman, Thomas F. 1950-, Cornell Theory Center.
The Physical Object
Pagination31 p. :
Number of Pages31
ID Numbers
Open LibraryOL16956777M

This paper describes and compares three parallel algorithms for solving sparse triangular systems of equations. These methods involve some preprocessing overhead and are primarily of interest in solving many systems with the same coefficient matrix. The first approach is to use a fixed blocksize and form the inverse of the diagonal blocks. @article{osti_, title = {Parallel and fault-tolerant algorithms for hypercube multiprocessors}, author = {Aykanat, C}, abstractNote = {Several techniques for increasing the performance of parallel algorithms on distributed-memory message-passing multi-processor systems are investigated. These techniques are effectively implemented for the parallelization of the Scaled Conjugate Gradient.

The performance of a fully parallel direct solver for large sparse-symmetric positive definite systems of linear equations is demonstrated. The solver is designed for distributed-memory, message-pa. hypercube parallel algorithm is going to memory parallelism in a multifrontal solver, Parallel Computing 40 (), pp , Multiprocessor im plementation model s for. adaptative.

Solving Triangular Systems 1 Forward Substitution Formulas processing the L of the LU factorization a third type of pipeline 2 Parallel Solving using an n-stage pipeline rewriting the formulas a parallel solver with OpenMP MCS Lecture 17 Introduction to Supercomputing Jan Verschelde, 30 September In this paper, we present a load balanced parallel sorting algorithm, balanced-sort, that runs in O((n log n)/p+p log2 n) average time for randomly distributed data on a hypercube multiprocessor. A d-dimensional hypercube multiprocessor (Fig. 1) is an MIMD .


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Parallel triangular solver for a hypercube multiprocessor by Guangye Li Download PDF EPUB FB2

We consider solving triangular systems of linear equations on a distributed-memory multiprocessor which allows for a ring embedding. Specifically, we propose a parallel algorithm, applicable when the triangular matrix is distributed by column in a wrap fashion.

Numerical experiments indicate that the new algorithm is very efficient in some circumstances (in particular, when the size of the Cited by: In this paper a new efficient parallel triangular solver for these problems is described.

This new algorithm is based on the previous method of Li and Coleman [] but is considerably more efficient when ${n / p}$ is relatively modest, where p is the number of processors, and n is the problem by: Efficient triangular solvers for use on message-passing multiprocessors are required, in several contexts, under the assumption that the matrix is distributed by columns (or rows) in a wrap fashion.

In this paper a new efficient parallel triangular solver for these problems is described. This new algorithm is based on the previous method of Li and Coleman [] but is considerably more Cited by: Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume ) A parallel triangular solver for a hypercube multiprocessor, SIAM J.

Sci. Stat. Comput., 9 (), pp. – Raghavan P. () Performance of Parallel Sparse Triangular Solution. In: Heath M.T., Ranade A., Schreiber R.S.

(eds) Algorithms Cited by: 4. Li and T.F. Coleman, A parallel triangular solver for a distributed memory multiprocessor, SIAM J. Stat. Comp. 9 (), pp. – MathSciNet CrossRef Google Scholar [8]Cited by: 2. Several parallel algorithms are presented for solving triangular systems of linear equations on distributed-memory multiprocessors.

New wavefront algorithms are developed for both row-oriented and column-oriented matrix storage. Performance of the new algorithms and several previously proposed algorithms is analyzed theoretically and illustrated empirically using implementations on.

Abstract. A parallel program for the solution of a triangular system of equations is formally derived. The program assumes the grid distribution of the n×n triangular matrix across p=Q 2 processes.

The complexity is n 2 /p+O (n), both for a complete and for a. Here we give a parallelLU decomposition method using block technique. The triangular systems are solved by using modified method of [1]. The numerical results are tested on Dawn multiprocessor system. From these results, we see that block technique is very important in matrix operations.

In our method of solving linear system, single processor can get 44MFOLPS, and 32 processors can get. The target architecture is a distributed-memory multiprocessor, and test results on an Intel iPSC/2 hypercube demonstrate the parallel efficiency of the algorithm.

A node system is measured to execute the algorithm over 48 times as fast as a single processor for the largest problem that fits on a single node (fixed size speedup).

@article{osti_, title = {Hypercube multiprocessors }, author = {Heath, M T}, abstractNote = {This book presents papers given at a conference on hypercube multiprocessors. Topics include the following: programming environments, language and data structures; operating systems; performance measurement; communication and architectural issues; and scientific applications.}, doi.

Parallel Computing 7 () North-Holland A parallel algorithm for sparse symbolic Cholesky factorization on a multiprocessor * Earl ZMIJEWSKI and John R. GILBERT Computer Science Department, Cornell University, Ithaca, NYU.S.A. Received July Revised April Albslraet.

A hypercube parallel computer is a network of processors, each with only local memory, whose activities are coordinated by messages the processors send between themselves.

A Parallel Triangular Solver for a Hypercube Multiprocessor. By Guangye Li and Thomas F. Coleman. Abstract. We consider solving triangular systems of linear equations on a hypercube multiprocessor. Specifically, we propose a fast parallel algorithm, applicable when the triangular matrix is distributed around the cube by column in a wrap.

We have implemented parallel triangular solve. with two task partitioning methods on a transputer -based multicomputer which contains. Ininos. T with 2 Mbytes of local memory. Our objective in this paper is the study of the parallel solution of the quasi-triangular matrix equation AXB + CXD = E, using coarse-grain algorithms on a shared memory multiprocessor with available BLAS routines [8].

Our approach extends the results obtained by Kågström, Nyström and Poromaa [14] for solving the triangular Sylvester matrix. A Parallel Triangular Solver for a Distributed-Memory Multiprocessor, G. Li and T. Coleman, SIAM Journal on Scientific and Statistical Computing, Vol.

9, No. 3, pp.A New Method for Solving Triangular Systems on Distributed-Memory Message-Passing Multiprocessor, G.

Li and T. Coleman, SIAM Journal on Scientific and Statistical. PARALLEL COMPUTING ELSEVIER Parallel Computing 20 () Parallel all-row preconditioned interval linear solver for nonlinear equations on multiprocessors Qi Gan a, Qing Yang a,*, Chenyi Hub a Dept.

of Electrical and Computer Engineering, The University of Rhode Island, Kingston, RIUSA b Dept. of Computer and Mathematical Sciences, University of Houston. The performance of a fully parallel direct solver for large sparse symmetric positive definite systems of linear equations is demonstrated. The solver is designed for distributed-memory message.

PARALLEL ALGORITHMS FOR THE QUASI-TRIANGULAR GENERAIJZED SYLVESTER MATRIX EQUATION ON A SHARED MEMORY MULTIPROCESSOR Mercedes Marques, Vicente Hernandez Departamento de Sisternas Ir{onnaticos y Conlputacion, Unil'ersidad Politecnica, Valencia, Spain ~ In this paper we discuss the resolution of the generalized Sylvester matrix equation.

A multiprocessor model is a generalization of the sequential RAM model in which there is more than one processor.

Multiprocessor models can be classified into three basic types: local memory machine models, modular memory machine models, and parallel random-access machine (PRAM) models. Figure 1 illustrates the structure of these machine models.

A Parallel Triangular Solver for a Hypercube Multiprocessor. The authors consider solving triangular systems of linear equations on a distributed-memory multiprocessor which allows for a .Numerical Experiments With an Overlapping Additive Schwarz Solver for 3-d pArallel Reservoir Simulation.

The International Journal of Supercomputer Applications and High Performance Computing, Vol. 9, Issue. 1, p. ‘ A parallel triangular solver on a distributed memory multiprocessor ’, SIAM J. Sci. Statist. S. and Vemulapati, U. L N. Hajj, S. Skelboe /Multilevelparallel solver for linear systems 31 6.

Parallel band matrix solver for hypercube Partitioning and allocation The principles of a multilevel parallel solver described in the previous sections were used for an implementation on the Intel iPSC hypercube.