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On Jacobi and Jacobi-like algorithms for a parallel computer

Author: Ahmed H. Sameh
Journal: Math. Comp. 25 (1971), 579-590
MSC: Primary 65D30
MathSciNet review: 0297131
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Abstract: Many existing algorithms for obtaining the eigenvalues and eigenvectors of matrices would make poor use of such a powerful parallel computer as the ILLIAC IV. In this paper, Jacobi's algorithm for real symmetric or complex Hermitian matrices, and a Jacobi-like algorithm for real nonsymmetric matrices developed by P. J. Eberlein, are modified so as to achieve maximum efficiency for the parallel computations.

References [Enhancements On Off] (What's this?)

  • [1] W. Bernhard, ILLIAC IV Codes for Jacobi and Jacobi-Like Algorithms, A Forthcoming Center for Advanced Computation Document, University of Illinois, Urbana, Illinois.
  • [2] R. L. Davis, ``The ILLIAC IV processing element,'' IEEE Trans. Computers, v. C-18, 1969, pp. 800-816.
  • [3] P. J. Eberlein, ``A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix,'' J. Soc. Indust. Appl. Math., v. 10, 1962, pp. 74-88. MR 25 #2699. MR 0139264 (25:2699)
  • [4] P. J. Eberlein & J. Boothroyd, ``Solution to the eigenproblem by a norm reducing Jacobi type method,'' Numer. Math., v. 11, 1968. pp. 1-12.
  • [5] H. H. Goldstine & L. P. Horwitz, ``A procedure for the diagonalization of normal matrices,'' J. Assoc. Comput. Mach., v. 6, 1959, pp. 176-195. MR 21 #426. MR 0101617 (21:426)
  • [6] P. Henrici, ``On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices,'' J. Soc. Indust. Appl. Math., v. 6, 1958, pp. 144-162. MR 20 #2084. MR 0095582 (20:2084)
  • [7] M. Knowles, B. Okawa, Y. Muroka & R. Wilhelmson, Matrix Operations on ILLIAC IV, ILLIAC IV Document #52, Dept. of Computer Science, University of Illinois, Urbana, Illinois, 1967.
  • [8] D. J. Kuck,"ILLIAC IV software and application programming,'' IEEE Trans. Computers, v. C-17, 1968, pp. 758-770.
  • [9] D. C. McIntyre, ``An introduction to the ILLIAC IV computer,'' Datamation, v. 16, No. 4, 1970, pp. 60-67.
  • [10] L. Mirsky, ``On the minimization of matrix norms,'' Amer. Math. Monthly, v. 65, 1958, pp. 106-107. MR 20 #3169. MR 0096686 (20:3169)
  • [11] A. Sameh & L. Han, Eigenvalue Problems, ILLIAC IV Document #127, Dept. of Computer Science, University of Illinois, Urbana, Illinois, 1968.
  • [12] D. L. Slotnick et al., ``The ILLIAC IV computer,'' IEEE Trans. Computers, v. C-17, 1968, pp. 746-757.
  • [13] J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965. MR 32 #1894. MR 0184422 (32:1894)

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Keywords: Parallel computers, ILLIAC IV, Jacobi's algorithm, Jacobi-like algorithm, orthogonal transformations, eigenvalues, eigenvectors, normal matrix
Article copyright: © Copyright 1971 American Mathematical Society

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