Abstract
The Singular Value Decomposition (SVD) is an algorithm that plays an essential role in many applications. There is a need for fast SVD algorithms in applications such as signal processing that require the SVD to be obtained or updated in real time. One technique for obtaining the SVD of a real dense matrix is to first reduce the dense matrix to bidiagonal form and then compute the SVD of the bidiagonal matrix. In this paper we describe how this approach can be implemented efficiently on the Connection Machine CM-5/CM-5E. Timing results show that use of the described techniques yields up to 45% of peak performance in the reduction from dense to bidiagonal form. Numerical results regarding the SVD computation of bidiagonal matrices illustrate that the approach considered yields accurate singular values as well as good performance. We also discuss the dependence between the accuracy of the singular values and the accuracy of the singular vectors.
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References
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
S. M. Balle & P. M. Pedersen, Singular Value Decomposition of Real Dense Matrices on the Connection Machine CM-5/CM-5E. in preparation (1994).
J. Demmel & W. Kahan, Accurate Singular Values of Bidiagonal Matrices, SIAM J. Sci. Stat. Comput. bf s11 (1990), pp. 873–912.
A. Edelman Large Dense Numerical Linear Algebra 1993, The Parallel Influence., Journal of Supercomputing Applications. 7, (1993), 113–128.
M. Metcalf & J. Reid, Fortran 8x Explained, Oxford Science Publications, Clarendon Press, Oxford, (1987).
G. H. Golub & C. F. Van Loan, Matrix Computations, 2. Ed., Johns Hopkins, (1989).
G. H. Golub & W. Kahan, Calculating the singular values and speudo-inverse of a matrix, SIAM J. NUMER. Anal. Seer. B, 2 (1965), pp. 205–224.
W. Lichtenstein & S. L. Johnsson, Block cyclic dense linear algebra, SIAM Journal of Scientific Computing v14:6 (1993), 1257–1286.
Thinking Machines Corporation, CM Fortran Libraries Reference Manual. Version 2.1, (1994).
Thinking Machines Corporation, The Connection Machine System, CMSSL for the CM5., (1993).
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© 1994 Springer-Verlag Berlin Heidelberg
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Balle, S.M., Pedersen, P.M. (1994). Singular Value Decomposition on the Connection Machine CM-5/CM-5E. In: Dongarra, J., Waśniewski, J. (eds) Parallel Scientific Computing. PARA 1994. Lecture Notes in Computer Science, vol 879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030134
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DOI: https://doi.org/10.1007/BFb0030134
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