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Block Algorithms for Parallel Machines

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Book cover Numerical Algorithms for Modern Parallel Computer Architectures

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 13))

Abstract

In this paper we discuss block methods in matrix computation and the role they are beginning to play on parallel computers.

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References

  1. Christian Bischof and Charles Van Loan. “The WY representation for products of Householder matrices.” Report TR-85–681, Cornell University Computer Science Department, 1985.

    Google Scholar 

  2. K.A. Braun and Th. Lunde Johnsen. “Hypermatrix generalization of the Jacobi and Eberlein method for computing eigenvalues and eigenvectors of hermitian and non-hermitian matrices.” Computer Methods in Applied Mechanics and Engineering 4 (1974) 1–18.

    Article  MathSciNet  MATH  Google Scholar 

  3. R.P. Brent and F.T. Luk. “The solution of singular value and symmetric eigenvalue problems on multiprocessor arrays.” SIAM Journal on Scientific and Statistical Computing 6 (1985) 69–84.

    Article  MathSciNet  MATH  Google Scholar 

  4. O.E. Brønlund and Th. Lunde Johnsen. “QR-factorization of partitioned matrices.” Computer Methods in Applied Mechanics and Engineering 3 (1974) 153–172.

    Article  MathSciNet  Google Scholar 

  5. J.J. Dongarra and D.C. Sorensen. “Linear algebra on high-performance computers.” In E. U. Schendel, editor, Proceedings Parallel Computing 85, 3–32. North Holland, 1986.

    Google Scholar 

  6. Gene H. Golub and Charles F. Van Loan. “Matrix Computations.” Johns Hopkins, 1983.

    MATH  Google Scholar 

  7. N. J. Higham. “Computing the polar decomposition — with applications.” SIAM Journal on Scientific and Statistical Computing 7 (1986) 1160–1174.

    Article  MathSciNet  MATH  Google Scholar 

  8. N.J. Higham. “Computing a nearest symmetric positive semi-definite matrix.” Numerical Analysis Report No. 126, University of Manchester Department of Mathematics, Nov. 1986.

    Google Scholar 

  9. Franklin T. Luk and Haesun Park. “A proof of convergence for two parallel Jacobi SVD algorithms.” Report EE-CEG-86–12, Cornell University School of Electrical Engineering, Nov. 1986.

    Google Scholar 

  10. V. Pan and J. Reif. “Efficient parallel solution of linear systems.” In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, (1985) 143–152.

    Chapter  Google Scholar 

  11. B. Parlett and R. Schreiber. “Block reflectors: Theory and computation.” SIAM Journal on Numerical Analysis, to appear.

    Google Scholar 

  12. R. Schreiber. “Computing generalized inverses and eigenvalues of symmetric matrices by systolic array.” in R. Glowinski and J. L. Lions, editors, Computer Methods in Applied Science and Engineering, 285–295. North-Holland, 1984.

    Google Scholar 

  13. R. Schreiber. “Solving eigenvalue and singular value problems on an undersized systolic array.” SIAM Journal on Scientific and Statistical Computing 7 (1986) 441–451.

    Article  MATH  Google Scholar 

  14. G. Schulz. “Iterative Berechnung der reziproken Matrix.” Z. Angew. Math. Mech. 13 (1933) 57–59.

    Article  MATH  Google Scholar 

  15. David S. Scott, Michael T. Heath and Robert C. Ward. “Parallel block Jacobi eigenvalue algorithms using systolic arrays.” Linear Algebra and Its Applications 77 (1986) 345–355.

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science Department, Rensselaer Polytechnic Institute, Troy, New York, 12180-3590, USA

    Robert Schreiber

Authors
  1. Robert Schreiber
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Editor information

Editors and Affiliations

  1. Research Center for Scientific Computation, Yale University, New Haven, CT, 06520, USA

    Martin Schultz

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© 1988 Springer-Verlag New York Inc.

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Schreiber, R. (1988). Block Algorithms for Parallel Machines. In: Schultz, M. (eds) Numerical Algorithms for Modern Parallel Computer Architectures. The IMA Volumes in Mathematics and Its Applications, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6357-6_12

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  • DOI: https://doi.org/10.1007/978-1-4684-6357-6_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-6359-0

  • Online ISBN: 978-1-4684-6357-6

  • eBook Packages: Springer Book Archive

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