BLOCK-JACOBI SVD ALGORITHMS FOR DISTRIBUTED MEMORY SYSTEMS I: HYPERCUBES AND RINGSFootnote*

* This work has been carried out within the framework of the research projects STABILE (INCO-COP96 0237) of the European Commission and Algorithmic Designs for Solving Some Problems of Parallel Numerics on Supercomputers of the Scientific Grant Agency of Slovak Republic and Slovak Academy of Sciences (VEGA).

References

• S.G. Akl , The Design ami Analysis of Parallel Algorithms . Prentice Hall . Englewood Cliffs . 1989 .
   Google Scholar
• P. Arbenz , Divide-and-conquer algorithms for the computation of the SVD of bidiagonal matrices . In Dongarra, J., Duff, I., Gaffney. P, and McKee, S. (Eds) , Vector anil Parallel Computing , Ellis Horwood , Chicester , 1989 , pp. 1 – 10 .
   Google Scholar
• C.H. Bischof , Computing the singular value decomposition on a distributed system of vector processors , TR-87-869 , Cornell University, Dept. of Comp. Science , 1987 .
   Google Scholar
• R.P. Brent and F.T. Luk , The solution of the singular value and symmetric eigenvalue problems on multiprocessor arrays , SIAM J, Sci. Statist. Compul . 6 ( 1985 ), 69 – 84 .
   Google Scholar
• T. Chan , An improved algorithm for computing the singular value decomposition , ACM Tram. Math. Software 8 ( 1982 ), 72 – 83 .
   Google Scholar
• S. Godet-Thobie , Eigenvalues of large highly nonnormal matrices , CERFACS Thesis Report THIPA/93106 , 1992 .
   Google Scholar
• S.K. Godunov , Spectral portrait of matrices and criteria of the spectrum dichotomy . In Herzberger, J. and Atanasova, A. (Eds) , Comp. Arithm. End. Melh. , North-Holland . 1991 .
   Google Scholar
• G.H. Golub and C. Reinsch , Singular value decomposition and least squares solutions , Numerische Mathematik 14 ( 1970 ), 403 – 420 .
   Web of Science ®Google Scholar
• G.H. Golub , CH.F. Van Loan , Matrix Computations , The John Hopkins University Press , Baltimore . 1989 .
   Google Scholar
• F.T. Luk , A triangular processor array for computing the SVD , Linear Algebra Appiic , 11 ( 1986 ), 259 – 274 .
   Google Scholar
• F.T. Luk and H. Park , On parallel Jacobi orderings , SIAM J. Sci. Statist. Comput . 10 ( 1989 ), 18 – 26 .
   Web of Science ®Google Scholar
• J.J. Modi and J.D. Pryce , Efficient implementation of Jacobi's diagonalization method on the DAP . Numer. Math . 46 ( 1985 ), 443 – 454 .
   Google Scholar
• Paragon System User's Guide, Intel Corporation, May , 1995 .
   Google Scholar
• A.H. Sameh , On Jacobi and Jacobi-like algorithms for a parallel computer . Math. Comp . 25 ( 1971 ), 579 – 590 .
   Web of Science ®Google Scholar
• G. Shroff and R. Schreiber , On the convergence of the cyclic Jacobi method for parallel block orderings , SIAM J. Sci. Statist. Comput . 10 ( 1989 ), 326 – 346 .
   Google Scholar
• M. Vajtersic , A fast SVD image restoration on an associative parallel computer . In Plander, I. (Ed.) , Proc. Artificial Intelligence and Information-Control Systems of Robots '84 , North-Holland , 1984 , pp. 383 – 387 .
   Google Scholar
• M. Vajtersic and M. Becka , Block-SVD algorithms and their adaptation to hypercubes and rings . In Mirenkov, N. (Ed.) , Proc. pAs97 International Conference , IEEE Press , 1997 , pp. 175 – 181 .
   Google Scholar
• B.B. Zhou and R.P. Brent , A parallel ring ordering algorithm for efficient one-sided Jacobi SVD computations , J. Parallel and Distributed Computing 42 ( 1997 ), 1 – 10 .
   Google Scholar
• * This work has been carried out within the framework of the research projects STABILE (INCO-COP96 0237) of the European Commission and Algorithmic Designs for Solving Some Problems of Parallel Numerics on Supercomputers of the Scientific Grant Agency of Slovak Republic and Slovak Academy of Sciences (VEGA).
   Google Scholar