Journal Article10.1007/BF02024486
A parallel interior point algorithm for linear programming on a network of transputers
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TL;DR: A parallel Dual Affine algorithm is presented which is suitable for a parallel computer with a distributed memory and obtains its speedup from parallel sparse linear algebra computations such as Cholesky factorisation, matrix multiplication, and triangular system solving.
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Abstract: Interior Point algorithms have become a very successful tool for solving large-scale linear programming problems The Dual Affine algorithm is one of the Interior Point algorithms implemented in the computer program OB1 It is a good candidate for implementation on a parallel computer because it is very computing-intensive A parallel Dual Affine algorithm is presented which is suitable for a parallel computer with a distributed memory The algorithm obtains its speedup from parallel sparse linear algebra computations such as Cholesky factorisation, matrix multiplication, and triangular system solving, which form the bulk of the computing work Efficient algorithms based on the grid distribution of matrices are presented for each of these computations The algorithm is implemented in occam 2 on a square mesh of transputers The resulting parallel program is connected to the sequentialFortran 77 program OB1, which performs the preprocessing and the postprocessing Experimental results on a mesh of 400 transputers are given for a test set of seven realistic planning and scheduling problems from Shell and seven problems from the NETLIB LP collection; the results show a speedup of 88 for the largest problem
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Citations
Developments and trends in the parallel solution of linear systems
Iain S. Duff,Henk A. van der Vorst +1 more
- 01 Dec 1999
TL;DR: This review paper considers some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism and considers preconditioning techniques for iterative solvers.
•Journal Article
Developments and trends in the parallel solution of linear systems
Iain S. Duff,HA van der Vorst +1 more
TL;DR: In this article, the authors consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism and discuss some of the present research issues in this field.
109
•Journal Article
Sparse numerical linear algebra: Direct methods and preconditioning
TL;DR: This talk discusses bisection and multisection techniques, extensions to orderings to block triangular form, and recent improvements and modifications to standard orderings such as minimum degree, as well as commenting on recent attempts to develop tools and platforms towards a sparse problem solving environment.
51
Exploiting Locality in Sparse Matrix-Matrix Multiplication on Many-Core Architectures
Kadir Akbudak,Cevdet Aykanat +1 more
TL;DR: Results show the validity of the models and methods proposed for enhancing the locality in parallel SpGEMM operations on a wide range of sparse matrices from real applications.
Simultaneous input and output matrix partitioning for outer-product-parallel sparse matrix-matrix multiplication
Kadir Akbudak,Cevdet Aykanat +1 more
TL;DR: Three hypergraph models are proposed that achieve simultaneous partitioning of input and output matrices without any replication of input data for outer-product--parallel sparse matrix-matrix multiplication (SpGEMM).
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On the Implementation of a Primal-Dual Interior Point Method
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