Journal Article10.1016/0167-8191(95)00011-C
The parallel QR factorization algorithm for tridiagonal linear systems
Pierluigi Amodio,Luigi Brugnano +1 more
- 01 Jul 1995
- Vol. 21, Iss: 7, pp 1097-1110
TL;DR: A new parallel solver in the class of partition methods for general, nonsingular tridiagonal linear systems, based on the QR factorization, which depends on the conditioning of the sub-blocks in each processor.
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Abstract: We describe a new parallel solver in the class of partition methods for general, nonsingular tridiagonal linear systems. Starting from an already known partitioning of the coefficient matrix among the parallel processors, we define a factorization, based on the QR factorization, which depends on the conditioning of the sub-blocks in each processor. Moreover, also the reduced system, whose solution is the only scalar section of the algorithm, has a dimension which depends both on the conditioning of these sub-blocks, and on the number of processors. We analyze the stability properties of the obtained parallel factorization, and report some numerical tests carried out on a net of transputers.
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Citations
Parallel solution of large symmetric tridiagonal linear systems
S. Chandra Sekhara Rao,Sarita +1 more
- 01 Mar 2008
TL;DR: A matrix factorization called WZ factorization for the solution of symmetric tridiagonal linear systems is presented and when combined with partitioning scheme, it renders a divide and conquer algorithm.
13
On the Stability of a Partitioning Algorithm for Tridiagonal Systems
Plamen Y. Yalamov,Velisar Pavlov +1 more
TL;DR: In the present paper, the second and third constants are bounded for some special classes of matrices, i.e., diagonally dominant (row or column), symmetric positive definite, M-matrices, and totally nonnegative.
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Parallel model order reduction based on block discrete Fourier transform and Krylov subspace for parametric systems
Zhen Li,Yao-Lin Jiang +1 more
TL;DR: In this paper , a time-domain parallel parametric model order reduction (PMOR) method for parametric systems based on the block discrete Fourier transform (DFT) and Krylov subspace is proposed.
7
Patent
Method of determining an intrinsic spectrum from a measured spectrum
Derk Reefman,William J. J. Rey,Augustus J. E. M. Janssen +2 more
- 30 May 2000
TL;DR: In this paper, the authors proposed a method to determine the eigenvalues of an NxN matrix of large dimensions (N of the order of from 10?4 to 105?). But it is not practical to use the maximum entropy algorithm.
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Algorithms for block bidiagonal systems on vector and parallel computers
Markus Hegland,Michael R. Osborne +1 more
- 13 Jul 1998
TL;DR: Parallel algorithms which combine high efficiency with good stability on vector and parallel computers are developed and it is suggested that methods combining tricyclic reduction-like steps with cyclic reductionlike steps lead to good performance.
3
References
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Introduction to Parallel and Vector Solution of Linear Systems
J. M. Ortega
- 30 Apr 1988
TL;DR: The Conjugate Gradient Algorithm and the Iterative Methods for Linear Equations are described, which simplify the derivation of linear algebra to simple linear algebra.
649
A Parallel Method for Tridiagonal Equations
TL;DR: A new (partition) method for solving a tndiagonal system of lmear equations is presented and various situations under which the partmon method can be preferable are described.
Solving tridiagonal systems on ensemble architectures
TL;DR: Partitioning the ensemble into subsets of processors is shown to be more efficient for the solution of multiple independent problems than pipelining the solutions over the entire ensemble.
135
Parallel factorizations for tridiagonal matrices
TL;DR: A wide class of efficient parallel solvers is derived by considering different parallel factorizations of partitioned matrices, and one of them derives a very efficient parallel method based on the cyclic reduction algorithm.
46
Parallelization and vectorization aspects of the solution of tridiagonal linear systems
Arno Krechel,Hans-Joachim Plum,Klaus Stüben +2 more
- 01 May 1990
TL;DR: This work presents several strategies for parallel solution of large tridiagonal systems on message-based MIMD computers with vector processors, theoretically as well as by concrete tests on the iPSC2-VX.
35
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