A new algorithm for diagonalizing a real symmetric matrix
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.
- 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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1093/comjnl/3.1.23
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.
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.
J. H. Wilkinson, “Householder’s method for the solution of the algebraic eigenvalue problem,” Comput. J. v. 3, 1960, p. 23-27.
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