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A new algorithm for diagonalizing a real symmetric matrix


Author: C. Donald LaBudde
Journal: Math. Comp. 18 (1964), 118-123
MSC: Primary 65.35
DOI: https://doi.org/10.1090/S0025-5718-1964-0160319-5
MathSciNet review: 0160319
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Abstract: The algorithm described in this paper is essentially a Jacobi-like procedure employing Householder and Jacobi orthogonal similarity transformations successively on a real symmetric matrix to obtain, in the limit, a diagonal matrix of eigenvalues. The columns of the product matrix of all the orthogonal transformations, taken in the proper order, form a complete orthonormal set of eigenvectors.


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

  • [1] G. E. Forsythe & P. Henrici, ``The cyclic Jacobi method for computing the principal values of a complex matrix,'' Trans. Amer. Math. Soc. v. 94, 1960, p. 1-23. MR 0109825 (22:710)
  • [2] H. H. Goldstine, F. M. Murray, & J. Von Neumann, ``The Jacobi method for symmetric matrices,'' J. Assoc. Comput. Mach., v. 6, 1959, p. 59-96. MR 0102171 (21:965)
  • [3] J. H. Wilkinson, ``Householder's method for the solution of the algebraic eigenvalue problem,'' Comput. J. v. 3, 1960, p. 23-27. MR 0111131 (22:1995)

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DOI: https://doi.org/10.1090/S0025-5718-1964-0160319-5
Article copyright: © Copyright 1964 American Mathematical Society

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