International Conference on Computational Science, 2001
During the past few years, algorithmic improvements alone have shaved almost an order of magnitud... more During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations. Combined with a similar increase in the performance to cost ratio due to hardware advances during this period, current sparse solver technology makes it possible to solve those problems quickly and easily that might have been considered impractically large until recently. In this paper, we compare the performance of some commonly used software packages for solving general sparse systems. In particular, we demonstrate the consistently high level of performance achieved by WSMP—the most recent of such solvers. We compare the various algorithmic components of these solvers and show that the choices made in WSMP enable it to run two to three times faster than the best amongst other similar solvers. As a result, WSMP can factor some of the largest sparse matrices available from real applications in a few seconds on 4-CPU workstation.
This report has been submitted for publication outside of IBM and will probably be copyrighted if... more This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution ...
International Conference on Computational Science, 2001
During the past few years, algorithmic improvements alone have shaved almost an order of magnitud... more During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations. Combined with a similar increase in the performance to cost ratio due to hardware advances during this period, current sparse solver technology makes it possible to solve those problems quickly and easily that might have been considered impractically large until recently. In this paper, we compare the performance of some commonly used software packages for solving general sparse systems. In particular, we demonstrate the consistently high level of performance achieved by WSMP—the most recent of such solvers. We compare the various algorithmic components of these solvers and show that the choices made in WSMP enable it to run two to three times faster than the best amongst other similar solvers. As a result, WSMP can factor some of the largest sparse matrices available from real applications in a few seconds on 4-CPU workstation.
Parallel Processing for Scientific Computing, 1995
Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In... more Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In this papei, we describe a parallel algorithm for sparse Cholesky factorization that incurs strictly less communication overhead than any known parallel formulation of sparse matrix ...
This report has been submitted for publication outside of IBM and will probably be copyrighted if... more This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution ...
Siam Journal on Matrix Analysis and Applications, 2001
Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct... more Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations.We have modified a classical sym-bolic factorization algorithm for unsymmetric matrices to inexpensively compute ...
Parallel Processing for Scientific Computing, 1995
Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In... more Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In this papei, we describe a parallel algorithm for sparse Cholesky factorization that incurs strictly less communication overhead than any known parallel formulation of sparse matrix ...
This paper describes an optimally scalable parallel algorithm for factorization of sparse matrice... more This paper describes an optimally scalable parallel algorithm for factorization of sparse matrices. This algorithm incurs strictly less communication overhead than any known parallel formulation of sparse matrix factorization, and hence, can utilize a higher number of ...
IEEE Transactions on Parallel and Distributed Systems, 1993
This paper provides a tutorial introduction to a performance evaluation metric called the isoeffi... more This paper provides a tutorial introduction to a performance evaluation metric called the isoefficiencyfunction. Traditional methods for evaluating serial algorithms are inadequate foranalyzing the performance of parallel algorithm-architecture combinations. Isoefficiency functionhas proven useful for evaluating the performance of a wide variety of such combinations
Siam Journal on Matrix Analysis and Applications, 2001
Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct... more Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations.We have modified a classical sym-bolic factorization algorithm for unsymmetric matrices to inexpensively compute ...
This paper describes an optimally scalable parallel algorithm for factorization of sparse matrice... more This paper describes an optimally scalable parallel algorithm for factorization of sparse matrices. This algorithm incurs strictly less communication overhead than any known parallel formulation of sparse matrix factorization, and hence, can utilize a higher number of ...
... Search: The ACM Digital Library The Guide. Feedback. Introduction to parallel computing: desi... more ... Search: The ACM Digital Library The Guide. Feedback. Introduction to parallel computing: design and analysis of algorithms. Purchase this Book. Source, Pages: 498. Year of Publication: 1994. ISBN:0-8053-3170-0. Authors, Vipin Kumar, Ananth Grama, Anshul Gupta, George Karypis ...
IEEE Transactions on Parallel and Distributed Systems, 1993
This paper provides a tutorial introduction to a performance evaluation metric called the isoeffi... more This paper provides a tutorial introduction to a performance evaluation metric called the isoefficiencyfunction. Traditional methods for evaluating serial algorithms are inadequate foranalyzing the performance of parallel algorithm-architecture combinations. Isoefficiency functionhas proven useful for evaluating the performance of a wide variety of such combinations
Parallel Numerical Computation with Applications, 1999
Many problems in engineering and scienti c domains require solving large sparse systems of linear... more Many problems in engineering and scienti c domains require solving large sparse systems of linear equations, as a computationally intensive step towards the nal solution. It has long been a challenge to develop e cient parallel formulations of sparse direct solvers due to several di erent complex steps involved in the process. In this paper, we describe PSPASES, one of the rst e cient, portable, and robust scalable parallel solvers for sparse symmetric positive de nite linear systems that we have developed. We discuss the algorithmic and implementation issues involved in its development; and present performance and scalability results on Cray T3E and SGI Origin 2000. PSPASES could solve the largest sparse system (1 million equations) ever solved by a direct method, with the highest performance (51 GFLOPS for Cholesky factorization) ever reported.
Abstract. A new parallel algorithm for solving positive definite sym-metric tridiagonal systems o... more Abstract. A new parallel algorithm for solving positive definite sym-metric tridiagonal systems of linear equations is presented. It generalizes to the band and block tridiagonal cases. It is called the middle p-way BABE (burn at both ends) algorithm~ It has a redundancy of two: The ...
Graph partitioning is a fundamental problem in several scientific and engineering applications, i... more Graph partitioning is a fundamental problem in several scientific and engineering applications, including task partitioning for parallel processing. In this paper, we describe heuristics that improve the state-of-the-art practical algorithms used in graph partitioning ...
International Conference on Computational Science, 2001
During the past few years, algorithmic improvements alone have shaved almost an order of magnitud... more During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations. Combined with a similar increase in the performance to cost ratio due to hardware advances during this period, current sparse solver technology makes it possible to solve those problems quickly and easily that might have been considered impractically large until recently. In this paper, we compare the performance of some commonly used software packages for solving general sparse systems. In particular, we demonstrate the consistently high level of performance achieved by WSMP—the most recent of such solvers. We compare the various algorithmic components of these solvers and show that the choices made in WSMP enable it to run two to three times faster than the best amongst other similar solvers. As a result, WSMP can factor some of the largest sparse matrices available from real applications in a few seconds on 4-CPU workstation.
This report has been submitted for publication outside of IBM and will probably be copyrighted if... more This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution ...
International Conference on Computational Science, 2001
During the past few years, algorithmic improvements alone have shaved almost an order of magnitud... more During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations. Combined with a similar increase in the performance to cost ratio due to hardware advances during this period, current sparse solver technology makes it possible to solve those problems quickly and easily that might have been considered impractically large until recently. In this paper, we compare the performance of some commonly used software packages for solving general sparse systems. In particular, we demonstrate the consistently high level of performance achieved by WSMP—the most recent of such solvers. We compare the various algorithmic components of these solvers and show that the choices made in WSMP enable it to run two to three times faster than the best amongst other similar solvers. As a result, WSMP can factor some of the largest sparse matrices available from real applications in a few seconds on 4-CPU workstation.
Parallel Processing for Scientific Computing, 1995
Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In... more Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In this papei, we describe a parallel algorithm for sparse Cholesky factorization that incurs strictly less communication overhead than any known parallel formulation of sparse matrix ...
This report has been submitted for publication outside of IBM and will probably be copyrighted if... more This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution ...
Siam Journal on Matrix Analysis and Applications, 2001
Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct... more Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations.We have modified a classical sym-bolic factorization algorithm for unsymmetric matrices to inexpensively compute ...
Parallel Processing for Scientific Computing, 1995
Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In... more Optimally Scalable Parallel Sparse Cholesky Factorization* Anshul Gupta* Vipin Kumar* Abstract In this papei, we describe a parallel algorithm for sparse Cholesky factorization that incurs strictly less communication overhead than any known parallel formulation of sparse matrix ...
This paper describes an optimally scalable parallel algorithm for factorization of sparse matrice... more This paper describes an optimally scalable parallel algorithm for factorization of sparse matrices. This algorithm incurs strictly less communication overhead than any known parallel formulation of sparse matrix factorization, and hence, can utilize a higher number of ...
IEEE Transactions on Parallel and Distributed Systems, 1993
This paper provides a tutorial introduction to a performance evaluation metric called the isoeffi... more This paper provides a tutorial introduction to a performance evaluation metric called the isoefficiencyfunction. Traditional methods for evaluating serial algorithms are inadequate foranalyzing the performance of parallel algorithm-architecture combinations. Isoefficiency functionhas proven useful for evaluating the performance of a wide variety of such combinations
Siam Journal on Matrix Analysis and Applications, 2001
Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct... more Abstract. We present algorithms for the symbolic and numerical factorization phases in the direct solution of sparse unsymmetric systems of linear equations.We have modified a classical sym-bolic factorization algorithm for unsymmetric matrices to inexpensively compute ...
This paper describes an optimally scalable parallel algorithm for factorization of sparse matrice... more This paper describes an optimally scalable parallel algorithm for factorization of sparse matrices. This algorithm incurs strictly less communication overhead than any known parallel formulation of sparse matrix factorization, and hence, can utilize a higher number of ...
... Search: The ACM Digital Library The Guide. Feedback. Introduction to parallel computing: desi... more ... Search: The ACM Digital Library The Guide. Feedback. Introduction to parallel computing: design and analysis of algorithms. Purchase this Book. Source, Pages: 498. Year of Publication: 1994. ISBN:0-8053-3170-0. Authors, Vipin Kumar, Ananth Grama, Anshul Gupta, George Karypis ...
IEEE Transactions on Parallel and Distributed Systems, 1993
This paper provides a tutorial introduction to a performance evaluation metric called the isoeffi... more This paper provides a tutorial introduction to a performance evaluation metric called the isoefficiencyfunction. Traditional methods for evaluating serial algorithms are inadequate foranalyzing the performance of parallel algorithm-architecture combinations. Isoefficiency functionhas proven useful for evaluating the performance of a wide variety of such combinations
Parallel Numerical Computation with Applications, 1999
Many problems in engineering and scienti c domains require solving large sparse systems of linear... more Many problems in engineering and scienti c domains require solving large sparse systems of linear equations, as a computationally intensive step towards the nal solution. It has long been a challenge to develop e cient parallel formulations of sparse direct solvers due to several di erent complex steps involved in the process. In this paper, we describe PSPASES, one of the rst e cient, portable, and robust scalable parallel solvers for sparse symmetric positive de nite linear systems that we have developed. We discuss the algorithmic and implementation issues involved in its development; and present performance and scalability results on Cray T3E and SGI Origin 2000. PSPASES could solve the largest sparse system (1 million equations) ever solved by a direct method, with the highest performance (51 GFLOPS for Cholesky factorization) ever reported.
Abstract. A new parallel algorithm for solving positive definite sym-metric tridiagonal systems o... more Abstract. A new parallel algorithm for solving positive definite sym-metric tridiagonal systems of linear equations is presented. It generalizes to the band and block tridiagonal cases. It is called the middle p-way BABE (burn at both ends) algorithm~ It has a redundancy of two: The ...
Graph partitioning is a fundamental problem in several scientific and engineering applications, i... more Graph partitioning is a fundamental problem in several scientific and engineering applications, including task partitioning for parallel processing. In this paper, we describe heuristics that improve the state-of-the-art practical algorithms used in graph partitioning ...
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