Bounds for eigenvalues of tridiagonal symmetric matrices computed by the LR method
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- Math. Comp. 16 (1962), 438-445 Request permission
References
- F. L. Bauer and A. S. Householder, Moments and characteristic roots, Numer. Math. 2 (1960), 42–53. MR 110188, DOI 10.1007/BF01386207
- Ky Fan and A. J. Hoffman, Lower bounds for the rank and location of the eigenvalues of a matrix, Contributions to the solution of systems of linear equations and the determination of eigenvalues, National Bureau of Standards Applied Mathematics Series, No. 39, U.S. Government Printing Office, Washington, D.C., 1954, pp. 117–130. MR 0064732
- Wallace Givens, Numerical computation of the characteristic values of a real symmetric matrix, Oak Ridge National Laboratory, Oak Ridge, Tenn., 1954. Rep. ORNL 1574. MR 0063771
- Peter Henrici, The quotient-difference algorithm, Nat. Bur. Standards Appl. Math. Ser. 49 (1958), 23–46. MR 94901
- Alston S. Householder and Friedrich L. Bauer, On certain methods for expanding the characteristic polynomial, Numer. Math. 1 (1959), 29–37. MR 100962, DOI 10.1007/BF01386370
- Tosio Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334–339. MR 38738, DOI 10.1143/JPSJ.4.334
- W. Kohn, A note on Weinstein’s variational method, Phys. Rev. (2) 71 (1947), 902–904. MR 21211
- Cornelius Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Research Nat. Bur. Standards 45 (1950), 255–282. MR 0042791
- David E. Muller, A method for solving algebraic equations using an automatic computer, Math. Tables Aids Comput. 10 (1956), 208–215. MR 83822, DOI 10.1090/S0025-5718-1956-0083822-0
- Heinz Rutishauser, Solution of eigenvalue problems with the $LR$-transformation, Nat. Bur. Standards Appl. Math. Ser. 1958 (1958), no. 49, 47–81. MR 90118
- Heinz Rutishauser, Über eine kubisch konvergente Variante der $LR$-Transformation, Z. Angew. Math. Mech. 40 (1960), 49–54 (German). MR 114295, DOI 10.1002/zamm.19600400109
- J. H. Wilkinson, The calculation of eigenvectors by the method of Lanczos, Comput. J. 1 (1958), 148–152. MR 102915, DOI 10.1093/comjnl/1.3.148
- J. H. Wilkinson, Rigorous error bounds for computed eigensystems, Comput. J. 4 (1961/62), 230–241. MR 129124, DOI 10.1093/comjnl/4.3.230
- 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 1962 American Mathematical Society
- Journal: Math. Comp. 16 (1962), 438-445
- MSC: Primary 65.40
- DOI: https://doi.org/10.1090/S0025-5718-1962-0163430-6
- MathSciNet review: 0163430