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A Scalable Eigenvalue Solver for Symmetric Tridiagonal Matrices (1994)  (Make Corrections)  (14 citations)
C. Trefftz, C. C. Huang, P. K. McKinley, T.-Y. Li, Z. Zeng
Parallel Computing



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Abstract: Both massively parallel computers and clusters of workstations are considered promising platforms for numerical scientific computing. This paper describes the first distributed-memory implementation of the split-merge algorithm, an eigenvalue solver for symmetric tridiagonal matrices that uses Laguerre's iteration and exploits the separation property in order to create independent subtasks. Implementations of the splitmerge algorithm on both an nCUBE-2 hypercube and a cluster of Sun... (Update)

Context of citations to this paper:   More

...by a considerable margin. Most importantly, our method is, in contrast to the highly serial QR algorithm, fully parallel and scalable [23]. For a general matrix S, magnitude of the eigenvalues of the pencil (T; S) can be arbitrarily large when S is nearly singular. It is,...

.... Preliminary results on parallel implementation show that the split merge algorithm possesses scalability to a large extent [21] for solving symmetric tridiagonal eigenproblems, which is the main building block for our algorithm. The parallel implementation of the...

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6:   The John Hopkins University Press (context) - Golub, Van Loan - 1989
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BibTeX entry:   (Update)

C. Trefftz, P. K. McKinley, C. C. Huang, T.-Y. Li, and Z. Zeng, "A scalable eigenvalue solver for symmetric tridiagonal matrices," in Proceedings of the 14th International Conference on Distributed Computing Systems, 1994. accepted to appear. http://citeseer.ist.psu.edu/article/trefftz94scalable.html   More

@article{ trefftz95scalable,
    author = "C. Trefftz and C. C. Huang and P. K. McKinley and T.-Y. Li and Z. Zeng",
    title = "A scalable eigenvalue solver for symmetric tridiagonal matrices",
    journal = "Parallel Computing",
    volume = "21",
    number = "8",
    pages = "1213--1240",
    year = "1995",
    url = "citeseer.ist.psu.edu/article/trefftz94scalable.html" }
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2441   The John Hopkins University Press (context) - Golub, Loan et al. - 1990
983   The Art of Scientific Computing (context) - Press, Flannery et al. - 1986
624   The Algebraic Eigenvalue Problem (context) - Wilkinson - 1965
587   PVM: A framework for parallel distributed computing - Sunderam - 1990
351   A survey of wormhole routing techniques in direct networks (context) - Ni, McKinley - 1993
262   Visualizing performance of parallel programs (context) - Heath, Etheridge - 1992
193   The torus routing chip (context) - Dally, Seitz - 1986
110   Portable Programs for Parallel Processors (context) - Boyle, Butler et al. - 1987
61   A divide and conquer method for the symmetric tridiagonal ei.. (context) - Cuppen - 1981
51   A fully parallel algorithm for the symmetric eigenvalue prob.. (context) - Dongarra, Sorensen - 1987
39   Network-based multicomputers: An emerging parallel architect.. - Kung, Sansom et al. - 1991
32   Solving the symmetric tridiagonal eigenvalue problem on the .. (context) - Ipsen, Jessup - 1990
29   Introduction to numerical linear algebra and optimisation (context) - Ciarlet - 1989
27   Parallel homotopy algorithm for the symmetric tridiagonal ei.. (context) - Li, Zhang et al. - 1991
17   A Collection of Matrices for Testing Computational Algorithm.. (context) - Gregory, Karney - 1978
14   A serial implementation of Cuppen's divide and conquer algor.. - Rutter - 1994
10   Efficient broadcast in all-port wormhole-routed hypercubes - McKinley, Trefftz - 1993
10   A parallel QR algorithm for symmetric tridiagonal matrices (context) - Sameh, Kuck - 1977
10   Design and implementation of multicast operations for ATM-ba.. - Huang, Kasten et al. - 1994
9   A parallel implementation of the symmetric tridiagonal qr al.. (context) - Arbenz, Gates et al. - 1992
9   Laguerre's iteration in solving the symmetric tridiagonal ei.. - Li, Zeng - 1993
9   A multiprocessor algorithm for the symmetric tridiagonal eig.. (context) - Lo, Philippe et al. - 1987
3   Applying parallel computer systems to solve symmetric tridia.. (context) - Lu, Qiao - 1992
2   Philadelphia PA: SIAM (context) - Anderson, Bai et al. - 1992
1   Parallel bisection for finding eigenvalues on vector and SIM.. (context) - Conroy, Podrazik - 1992
1   A stable algorithm for the rank-1 modification of the symmet.. (context) - Gu, Eisenstat - 1992
1   Effects of Communication Costs on the Design and Implementat.. (context) - Trefftz - 1994
1   Efficient, massively parallel eigenvalue computation (context) - Huo, Schreiber - 1993



The graph only includes citing articles where the year of publication is known.


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