A Parallel Ring Ordering Algorithm for Efficient One-Sided Jacobi SVD Computations

Journal of Parallel and Distributed Computing

Volumn 42, Issue 1, 1997, Pages 1-10

  Zhou, B B ^a   Brent, R P ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038460094     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.1997.1304     Document Type: Article

References (25)

1. Akl S. G. Parallel Sorting Algorithms. 1985;Academic Press, Orlando.
2. Baudet G., Stevenson D. Optimal sorting algorithms for parallel computers. IEEE Trans. Comput. 27:1978;84-87.
3. Bischof C. H. The two-sided block Jacobi method on a hypercube. Hypercube Multiprocessors. 1988;SIAM, Philadelphia. p. 612-618.
4. R. P. Brent, Aug. 1988, Parallel algorithms for digital signal processing, Proceedings of the NATO Advanced Study Institute on Numerical Linear Algebra, Digital Signal Processing and Parallel Algorithms, 93, 110, Leuven, Belgium.
5. Brent R. P., Luk F. T. The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays. SIAM J. Sci. Stat. Comput. 6:1985;69-84.
6. Demmel J., Veselić K. Jacobi's method is more accurate than QR. SIAM J. Sci. Statist. Comput. 11:1992;1204-1246.
7. Eberlein P. J., Park H. Efficient implementation of Jacobi algorithms and Jacobi sets on distributed memory architectures. J. Parallel Distrib. Comput. 8:1990;358-366.
8. Ewerbring L. M., Luk F. T. Computing the singular value decomposition on the Connection Machine. IEEE Trans. Comput. 39:1990;152-155.
9. Forsythe G. E., Henrici P. The cyclic Jacobi method for computing the principal values of a complex matrix. Trans. Amer. Math. Soc. 94:1960;1-23.
10. G. R. Gao, S. J. Thomas, 1988, An optimal parallel Jacobi-like solution method for the singular value decomposition, Proc. Internat. Conf. Parallel Proc. 47, 53.
11. Golub G. H., Van Loan C. F. Matrix Computations. 1989;Johns Hopkins Univ. Press, Baltimore.
12. Henrici P. On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices. J. Soc. Indust. Appl. Math. 6:1958;144-162.
13. Hestenes M. R. Inversion of matrices by biorthogonalization and related results. J. Soc. Indust. Appl. Math. 6:1958;51-90.
14. Hüper K., Helmke U. Structure and convergence of Jacobi-type methods. Tech. Report. TUM-LNS-TR-95-02:1995.
15. Lee T. J., Luk F. T., Boley D. L. Computing the SVD on a Fat-Tree Architecture. Report. 92-33:Nov. 1992.
16. Leiserson C. E. Fat-trees: Universal networks for hardware-efficient supercomputing. IEEE Trans. Comput. 34:1985;892-901.
17. Luk F. T. Computing the singular-value decomposition on the ILLIAC IV. ACM Trans. Math. Software. 6:1980;524-539.
18. Luk F. T. A triangular processor array for computing singular values. Linear Algebra Appl. 77:1986;259-273.
19. Luk F. T., Park H. On parallel Jacobi orderings. SIAM J. Sci. Statist Comput. 10:1989;18-26.
20. Nash J. C. A one-sided transformation method for the singular value decomposition and algebraic eigenproblem. Comput. J. 18:1975;74-76.
21. De Rijk P. P. M. A one-sided Jacobi Algorithm for computing the singular value decomposition on a vector computer. SIAM J. Sci. Statist Comput. 10:1989;359-371.
22. Schreiber R. Solving eigenvalue and singular value problems on an undersized systolic array. SIAM J. Sci. Statist Comput. 7:1986;441-451.
23. Veselić K., Hari V. A note on a one-sided Jacobi algorithm. Numer. Math. 56:1990;627-633.
24. Wilkinson J. H. The Algebraic Eigenvalue Problem. 1965;Clarendon Press, Oxford. p. 277-278.
25. B. B. Zhou, R. P. Brent, Jan. 1995, On the parallel implementations of the one-sided Jacobi algorithm for singular value decompositions, Proc. of 3rd Euromicro Workshop on Parallel and Distributed Processing, 401, 408, San Remo, Italy.