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A Proof of Convergence for Two Parallel Jacobi SVD Algorithms
June 1989 (vol. 38 no. 6)
pp. 806-811
The authors consider two parallel Jacobi algorithms, due to R.P. Brent et al. (J. VLSI Comput. Syst., vol.1, p.242-70, 1985) and F.T. Luk (1986 J. Lin. Alg. Applic., vol.77, p.259-73), for computing the singular value decomposition of an n*n matrix. By relating the algorithms to the cyclic-by-rows Jacobi method, they prove convergence of the former for odd n and of the latter for any n. The aut

[1] R. P. Brent and F. T. Luk, "The solution of singular-value and symmetric eigenvalue problems on multiprocessor arrays,"SIAM J. Sci. Statist. Comput., vol. 6, pp. 69-84, 1985.
[2] R. P. Brent, F. T. Luk, and C. F. Van Loan, "Computation of the singular value decomposition using mesh-connected processors,"J. VLSI Comput. Syst., vol. 1, pp. 242-270, 1985.
[3] G. E. Forsythe and P. Henrici, "The cyclic Jacobi method for computing the principal values of a complex matrix,"Trans. Amer. Math. Soc., vol. 94, pp. 1-23, 1960.
[4] W. M. Gentleman, "Error analysis of QR decompositions by Givens transformations,"J. Lin. Alg. Appl., vol. 10, pp. 189-197, 1975.
[5] E. R. Hansen, "On cyclic Jacobi methods,"J. SIAM, vol. 11, pp. 448-459, 1963.
[6] F. T. Luk, "A triangular processor array for computing singular values,"J. Lin. Alg. Appl., vol. 77, pp. 259-273, 1986.
[7] F. T. Luk and H. Park, "On parallel Jacobi orderings,"SIAM J. Sci. Statist. Comput., vol. 1, pp. 18-26, 1989.
[8] J. J. Modi and J. D. Pryce, "Efficient implementation of Jacobi's diagonalization method on the DAP,"Numer. Math., vol. 46, pp. 443-454, 1985.
[9] H. Park, "On the equivalence and convergence of parallel Jacobi SVD algorithms," Ph.D. dissertation, Dep. Comput. Sci., Cornell Univ., 1987.
[10] A. Sameh, "Solving the linear least squares problem on a linear array of processors," inAlgorithmically Specialized Parallel Computers, L. Snyder, L. Jamieson, D. Gannon, and H. Siegel, Eds. New York: Academic, 1985, pp. 191-200.
[11] U. Schwiegelshohn and L. Thiele, "A systolic array for cyclic-by-rows Jacobi algorithms,"J. Parallel Distrib. Comput., vol. 4, pp. 334- 340, 1987.
[12] G. W. Stewart, "A Jacobi-like algorithm for computing the Schur decomposition of a non-Hermitian matrix,"SIAM J. Sci. Statist. Comput., vol. 6, pp. 853-864, 1985.
[13] J. J. Symanski, "Architecture of the systolic linear algebra parallel processor," inReal Time Signal Processing IX, W. J. Miceli, Ed.,Proc. SPIE, vol. 698, 1986, pp. 17-22.
[14] R. A. Whiteside, N. S. Ostlund, and P. G. Hibbard, "A parallel Jacobi diagonalization algorithm for a loop multiple processor system,"IEEE Trans. Comput., vol. C-33, pp. 409-413, 1984.

Index Terms:
convergence; Jacobi SVD algorithms; parallel Jacobi algorithms; singular value decomposition; convergence of numerical methods; matrix algebra; parallel algorithms.
Citation:
F.T. Luk, H. Park, "A Proof of Convergence for Two Parallel Jacobi SVD Algorithms," IEEE Transactions on Computers, vol. 38, no. 6, pp. 806-811, June 1989, doi:10.1109/12.24289
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