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International Journal of Computer Mathematics Volume 16, 1984 - Issue 4
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Original Articles

Parallel algorithms for the solution of certain large sparse linear systems

M. Benson Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada
,
J. Krettmann Graduate Studies, Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
&
M. Wright Undergraduate Studies, Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, Canada
Pages 245-260 | Received 01 Dec 1983, Published online: 19 Mar 2007

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J. D. F. Cosgrove, J. C. Díaz & A. Griewank. (1992) Approximate inverse preconditionings for sparse linear systems . International Journal of Computer Mathematics 44:1-4, pages 91-110.
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RabindraN. Banerjee & Maurice W. Benson. (1991) An approximate inverse based multigrid approach to the biharmonic problem. International Journal of Computer Mathematics 40:3-4, pages 201-210.
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Maurice W. Benson. (1990) Frequency domain behavior of a set of parallel multigrid smoothing operators. International Journal of Computer Mathematics 36:1-2, pages 77-88.
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Articles from other publishers (22)

Jonathan E Moussa & Andrew D Baczewski. (2019) Assessment of localized and randomized algorithms for electronic structure. Electronic Structure 1:3, pages 033001.
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Zhongxiao Jia & Wenjie Kang. (2019) A transformation approach that makes SPAI, PSAI and RSAI procedures efficient for large double irregular nonsymmetric sparse linear systems. Journal of Computational and Applied Mathematics 348, pages 200-213.
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Zhongxiao Jia & Wenjie Kang. (2017) A residual based sparse approximate inverse preconditioning procedure for large sparse linear systems. Numerical Linear Algebra with Applications 24:2, pages e2080.
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Luis González, Antonio Suárez & Eduardo Rodríguez. (2014) A generalization of the optimal diagonal approximate inverse preconditioner. Computers & Mathematics with Applications 66:12, pages 2433-2445.
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M. M. Dehnavi, D. M. Fernandez, J. Gaudiot & D. D. Giannacopoulos. (2013) Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units. IEEE Transactions on Parallel and Distributed Systems 24:9, pages 1852-1862.
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Zhongxiao Jia & Baochen Zhu. (2008) A power sparse approximate inverse preconditioning procedure for large sparse linear systems. Numerical Linear Algebra with Applications 16:4, pages 259-299.
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KENGO NAKAJIMA. (2011) SPARSE APPROXIMATE INVERSE PRECONDITIONER FOR CONTACT PROBLEMS ON THE EARTH SIMULATOR USING OPENMP. International Journal of Computational Methods 05:02, pages 255-272.
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Ruth M. Holland, Andy J. Wathen & Gareth J. Shaw. (2005) Sparse Approximate Inverses and Target Matrices. SIAM Journal on Scientific Computing 26:3, pages 1000-1011.
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Baolai Ge. 2005. Current Trends in High Performance Computing and Its Applications. Current Trends in High Performance Computing and Its Applications 37 46 .
B. Carpentieri, I. S. Duff, L. Giraud & M. Magolu monga Made. (2004) Sparse symmetric preconditioners for dense linear systems in electromagnetism. Numerical Linear Algebra with Applications 11:8-9, pages 753-771.
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Kai Wang, Sang-Bae Kim, Jun Zhang, Kengo Nakajima & Hiroshi Okuda. (2003) Global and localized parallel preconditioning techniques for large scale solid Earth simulations. Future Generation Computer Systems 19:4, pages 443-456.
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Kai Wang & Jun Zhang. (2003) MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies. SIAM Journal on Scientific Computing 24:4, pages 1141-1156.
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Annamaria Mazzia & Giorgio Pini. (2002) Numerical performance of preconditioning techniques for the solution of complex sparse linear systems. Communications in Numerical Methods in Engineering 19:1, pages 37-48.
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Edmond Chow. (2016) Parallel Implementation and Practical Use of Sparse Approximate Inverse Preconditioners with a Priori Sparsity Patterns. The International Journal of High Performance Computing Applications 15:1, pages 56-74.
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B. Carpentieri, I. S. Duff & L. Giraud. (2000) Sparse pattern selection strategies for robust Frobenius-norm minimization preconditioners in electromagnetism. Numerical Linear Algebra with Applications 7:7-8, pages 667-685.
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D.J. Brown & R.M. Stringfield. (2000) Iterative Methods Applied to Matrix Equations Found in Calculating Spheroidal Functions. Journal of Computational Physics 159:2, pages 329-343.
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Michele Benzi & Miroslav Tuma. (1998) A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems. SIAM Journal on Scientific Computing 19:3, pages 968-994.
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Ivar Gustafsson & Gunhild Lindskog. (2005) Completely parallelizable preconditioning methods. Numerical Linear Algebra with Applications 2:5, pages 447-465.
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I. E. Kaporin. (2005) New convergence results and preconditioning strategies for the conjugate gradient method. Numerical Linear Algebra with Applications 1:2, pages 179-210.
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R.D. Smith, J.K. Dukowicz & R.C. Malone. (1992) Parallel ocean general circulation modeling. Physica D: Nonlinear Phenomena 60:1-4, pages 38-61.
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J.C. Diaz & T. Mansfield. (1990) Connection Machine implementation of an appropriate inverse preconditioning with minimum residual iteration. Connection Machine implementation of an appropriate inverse preconditioning with minimum residual iteration.
A. Greenbaum & G. H. Rodrigue. (1989) Optimal preconditioners of a given sparsity pattern. BIT 29:4, pages 610-634.
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