摘要:

We set up a class of parallel multisplilting relaxed methods for the system of nonlinear equationsAϕ(u) + Tψ(u) = G(u) withA,TϵL(Rn),ϕ,ψ:Rn → Rnbeing diagonal mappings andG: Rn → Rnbeing a general mapping, which is generally resulted from the discretization of many classical differential equations. Under rather proper conditions, we confirm the existence and uniqueness of the solution of this system of equations, and establish the global convergence theories for the new methods.

ISSN:1063-7192    

DOI:10.1080/10637199508915518

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The philosophy of multisplitting methods is the replacement of a large-scale linear or nonlinear problem by a set of subproblems, each of which can be solved locally and independently in parallel by taking advantage of well-tested sequential algorithms. Because of this formulation most compute-intensive operations can be calculated independently and the algorithms are highly parallel. Recent developments for optimization, constrained and unconstrained, are described. These new algorithms are, in some cases, faster in sequential mode than conventional algorithms. Results of implementations on the Intel Paragon and on a cluster of workstations using PVM3 demonstrate superlinear speedup when compared with a standard test algorithm programmed in sequential mode. Further, the same algorithm when programmed in sequential mode also exhibits speedup when compared to the non-split algorithm.

ISSN:1063-7192    

DOI:10.1080/10637199508915519

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

For modern public key cryptographic systems, the modular cascade exponentiation ((πi=1pxini)modu) is one of the most important arithmetic fundamentals to ensure security. However, the large computing effort needed by this operation also causes the cryptosystems inefficient. The purpose of this paper is to develop some fast methods for computing the modular cascade exponentiation. Two new parallel schemes, called the parallel multi-dimensional binary method and the parallel merging binary method, are proposed. The concept of the shortest parallel vectorial addition chain, which is an optimal approach for parallel computing the modular cascade exponentiation, is also given. The two proposed parallel schemes are faster than the best known serial or parallel modular cascade exponentiation methods. In addition, the computation time of the proposed parallel merging binary method is very close to the lower bound of the shortest parallel vectorial addition chain.

ISSN:1063-7192    

DOI:10.1080/10637199508915520

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

The well knownQRfactorisation methods for solving linear systems is compared with theQZorthogonal decomposition method [2]. Timings on a shared memory parallel computer confirm the superiority of the latter method by up to 14% for large linear systems for both sequential and parallel implementations.

ISSN:1063-7192    

DOI:10.1080/10637199508915521

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this paper we extend the 4-point explicit de-coupled group (EDG) iterative method, Abdullah (1991), to the 6 and 9-poinl EDG methods for the solution of elliptic partial differential equations. We will show graphically the technique of implementing the new grouping. Performance results for the algorithms are presented and a comparison with the 4-point scheme confirm the new groups to be computationally superior. Further, the implementations of the parallel 4, 6 and 9-point EDG methods on the Sequent Balance 8000 multiprocessor arc discussed and results from experiments performed are presented.

ISSN:1063-7192    

DOI:10.1080/10637199508915522

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

ISSN:1063-7192    

DOI:10.1080/10637199508915523

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

This paper discusses the application of folding techniques on systolic matrix vector iterations performed on re-usable linear systolic arrays. The matrix vector iterations are presented in the context of well known linear algebra iterative methods for the solution of systems of equations. The same iterations form the basis of relaxation procedures of Hopfield type artificial neural networks.

ISSN:1063-7192    

DOI:10.1080/10637199508915524

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this paper, we study the problem of scheduling loop task graphs onto two processor systems to minimize the execution lime. We use the idea of loop unrolling to uncover dependence among different loop iterations in loop task graphs. The scheduling is divided into two stages: determining an optimal unrolling factor, and constructing an optimal schedule for this unrolling factor. We propose a criterion for optimal loop unrolling for unit-delay task graphs, where the tasks are enclosed in a single loop. Our main theorem presents a useful test for detecting optimal unrolling factors. A scheduling algorithm that employs the concept of optimal loop unrolling is introduced. We also present serial and parallel algorithms lo find the best unrolling factor.

ISSN:1063-7192    

DOI:10.1080/10637199508915525

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

In this paper we have given a parallel algorithm to solve Singularly perturbed boundary value problems. This algorithm is designed on the basis ofWDZFactorization and parallel prefix algorithm. We have given the algorithm for both limited and unlimited processors.

ISSN:1063-7192    

DOI:10.1080/10637199508915526

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor

摘要:

Among the several methods for solving linear matrix equations, the Hessenberg-Schur method is one of the most efficient sequential algorithms. In a previous work, we developed parallel algorithms, based on this method, for solving the Sylvester matrix equation. In this work we propose a modification of our algorithm which reduces the cost by reordering a special coefficient matrix that has to be triangularized. The defined reordering allows a regular distribution of the data in the parallel algorithm. Both a complexity analysis and an experimental study of the algorithm are also presented.

ISSN:1063-7192    

DOI:10.1080/10637199508915527

出版商:Taylor & Francis Group    

年代:1995

数据来源: Taylor