A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations.
Ghodsi, Seyed Roholah, Taeibi-Rahni, Mohammad (2010)
Mathematical Problems in Engineering
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Displaying similar documents to “A nested decomposition algorithm for parallel computations of very large sparse systems.”
A novel parallel algorithm based on the Gram-Schmidt method for tridiagonal linear systems of equations.
A decomposition-based control strategy for large, sparse dynamic systems.
Zečević, Aleksandar I., Šiljak, Dragoslav D. (2005)
Mathematical Problems in Engineering
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A parallel block Lanczos algorithm and its implementation for the evaluation of some eigenvalues of large sparse symmetric matrices on multicomputers
Mario Guarracino, Francesca Perla, Paolo Zanetti (2006)
International Journal of Applied Mathematics and Computer Science
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In the present work we describe HPEC (High Performance Eigenvalues Computation), a parallel software package for the evaluation of some eigenvalues of a large sparse symmetric matrix. It implements an efficient and portable Block Lanczos algorithm for distributed memory multicomputers. HPEC is based on basic linear algebra operations for sparse and dense matrices, some of which have been derived by ScaLAPACK library modules. Numerical experiments have been carried out to evaluate HPEC...
Parallel Processing on Block-based Gauss-Jordan Algorithm for Desktop Grid
Yizi Shang, Guiming Lu, Ling Shang, Guangqian Wang (2011)
Computer Science and Information Systems
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An algorithm for model reduction in large electric power systems.
Zečević, A.I., Gačić, N. (1998)
Mathematical Problems in Engineering
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A variant of the reciprocal super Catalan matrix
Emrah Kılıç, Ilker Akkus, Gonca Kızılaslan (2015)
Special Matrices
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Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formulæ for its LU-decomposition, LUdecomposition of its inverse and the Cholesky decomposition are obtained. For all...
Implementing parallel elliptic solver on a Beowulf cluster.
Paprzycki, Marcin, Petrova, Svetozara, Sanchez, Julian (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Joint domain-decomposition -LU preconditioners for saddle point problems.
Le Borne, Sabine, Oliveira, Suely (2007)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Direct methods for matrix Sylvester and Lyapunov equations.
Sorensen, Danny C., Zhou, Yunkai (2003)
Journal of Applied Mathematics
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Influence of preconditioning and blocking on accuracy in solving Markovian models
Beata Bylina, Jarosław Bylina (2009)
International Journal of Applied Mathematics and Computer Science
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The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative...
Locality of reference in sparse Cholesky factorization methods.
Rozin, Elad, Toledo, Sivan (2005)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
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Parallel QR Decomposition of a Rectangular Matrix.
M. Cosnard, J.-M. Muller, Y. Robert (1986)
Numerische Mathematik
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A new block triangular preconditioner for three-by-three block saddle-point problem
Jun Li, Xiangtuan Xiong (2024)
Applications of Mathematics
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In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties...