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Parallel Computation of the SVD of a Matrix Product

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Book cover Recent Advances in Parallel Virtual Machine and Message Passing Interface (EuroPVM/MPI 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1697))

Abstract

In this paper we studya parallel algorithm for computing the singular value decomposition (SVD) of a product of two matrices on message passing multiprocessors. This algorithm is related to the classical Golub-Kahan method for computing the SVD of a single matrix and the recent work carried out byGolu b et al. for computing the SVD of a general matrix product/quotient. The experimental results of our parallel algorithm, obtained on a network of PCs and a SUN Enterprise 4000, show high performances and scalabilityfor large order matrices.

This research was partiallys upported by the Spanish CICYT project under grant TIC96-1062-C03-01-03.

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References

  1. Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., Mckenney, A., Ostrouchov, S., Sorensen, D.: LAPACK User’s Guide, Release 1.0., SIAM, Philadelphia (1992).

    Google Scholar 

  2. Bai, Z: A parallel algorithm for computing the generalized singular value decomposition, Journal of Parallel and Distributed Computing 20 (1994) 280–288.

    Article  MATH  Google Scholar 

  3. Brent, R., Luk, F. and van Loan, C.: Computation of the generalized singular value decomposition using mesh connected processors, Proc. SPIE Vol. 431, Real time signal processing VI (1983) 66–71.

    Google Scholar 

  4. Blackford, L., Choi, J., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, L., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.: SCALAPACK User’s Guide, SIAM (1997).

    Google Scholar 

  5. De Moor, B. and Golub, G. H.: Generalized singular value decompositions: A proposal for a standardized nomenclature, Num. Anal. Proj. Report 89-04, Comput. Sci. Dept., Stanford University(1989).

    Google Scholar 

  6. De Moor, B.: On the structure and geometryof the PSVD, Num. Anal. Project, NA-89-05, Comput. Sci. Dept., Stanford University (1989).

    Google Scholar 

  7. Demmel, J., Kahan, W.: Accurate singular values of bidiagonal matrices, SIAM J. Sci. Stat. Comput. 11 (1990) 873–912.

    Article  MATH  MathSciNet  Google Scholar 

  8. Fernando, K. and Hammarling, S.: A generalized singular value decomposition for a product of two matrices and balanced realization, NAG Technical Report TR1/87, Oxford (1987).

    Google Scholar 

  9. Fernando, K. and Parlett, B.: Accurate singular values and differential qd algorithms. Numerische Mathematik 67 (1994) 191–229.

    Article  MATH  MathSciNet  Google Scholar 

  10. Golub, G., W. Kahan, Calculation of the singular values and the pseudoinverse of a matrix, SIAM J. Numer. Anal. 2 (1965) 205–224.

    Article  MathSciNet  Google Scholar 

  11. Golub, G., Reinsch, W.: Singular value decomposition and the least square solution, Numer. Mathematik 14, (1970) 403–420.

    Article  MATH  MathSciNet  Google Scholar 

  12. Golub, G., Sølna, K, and van Dooren, P.: Computing the SVD of a General Matrix Product/Quotient, submitted to SIAM J. on Matrix Anal. & Appl.,(1997).

    Google Scholar 

  13. Golub, G., Van Loan, C.: Matrix Computations, North Oxford Academic, Oxford (1983).

    MATH  Google Scholar 

  14. Heat, M., Laub, A., Paige, C., Ward, R.: Computing the singular value decomposition of a product of two matrices, SIAM J. Sci. Stat. Comput. 7 (1986) 1147–1159.

    Article  Google Scholar 

  15. Laub, A., Heat, M., Paige, G., Ward, R.: Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms, IEEE Trans. AC 32 (1987) 115–122.

    MATH  Google Scholar 

  16. Mollar, M., Hernández, V.: Computing the singular values of the product of two matrices in distributed memory multiprocessors, Proc. 4th Euromicro Workshop on Parallel and Distributed Computation, Braga (1996) 15–21.

    Google Scholar 

  17. Mollar, M., Hernández, V.: A parallel implementation of the singular value decomposition of the product of triangular matrices, 1st NICONET Workshop, Valencia (1998)

    Google Scholar 

  18. Moore, B.: Principal component analysis in linear systems: Controlability, observability, and model reduction, IEEE Trans. AC 26 (1981) 100–105.

    Google Scholar 

  19. Paige, C., Sanders, M.: Towards a generalized singular value decomposition, SIAM J. Numer. Anal. 18 (1981) 398–405.

    Article  MATH  MathSciNet  Google Scholar 

  20. Van Loan, C.: Generalizing the singular value decomposition, SIAM J. Numer. Anal. 13 (1976) 76–83.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Dpto. de Informática, Univ. Jaume I, E-12080, Castellón, Spain

    Josée M. Claver & Manuel Mollar

  2. Dpto. de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, E-46071, Valencia, Spain

    Vicente Hernández

Authors
  1. Josée M. Claver
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  2. Manuel Mollar
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  3. Vicente Hernández
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Editor information

Editors and Affiliations

  1. OakRidge National Laboratory, University of Tennessee, 107, Ayres Hall, Knoxville, TN, 37996-1301, USA

    Jack Dongarra

  2. Computer Science Department Computer Architecture and Operating Systems Group, Universitat Autònoma of Barcelona, E-08193, Bellaterra, Barcelona, Spain

    Emilio Luque  & Tomàs Margalef  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Claver, J.M., Mollar, M., Hernández, V. (1999). Parallel Computation of the SVD of a Matrix Product. In: Dongarra, J., Luque, E., Margalef, T. (eds) Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 1999. Lecture Notes in Computer Science, vol 1697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48158-3_48

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  • DOI: https://doi.org/10.1007/3-540-48158-3_48

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66549-6

  • Online ISBN: 978-3-540-48158-4

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