A new algorithm for diagonalizing a real symmetric matrix
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- by C. Donald LaBudde PDF
- Math. Comp. 18 (1964), 118-123 Request permission
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
- G. E. Forsythe and P. Henrici, The cyclic Jacobi method for computing the principal values of a complex matrix, Trans. Amer. Math. Soc. 94 (1960), 1–23. MR 109825, DOI 10.1090/S0002-9947-1960-0109825-2
- H. H. Goldstine, F. J. Murray, and J. von Neumann, The Jacobi method for real symmetric matrices, J. Assoc. Comput. Mach. 6 (1959), 59–96. MR 102171, DOI 10.1145/320954.320960
- J. H. Wilkinson, Householder‘s method for the solution of the algebraic eigenproblem, Comput. J. 3 (1960/61), 23–27. MR 111131, DOI 10.1093/comjnl/3.1.23
Additional Information
- © Copyright 1964 American Mathematical Society
- 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