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References
Jane Cullum and Ralph A. Willoughby (1979), Fast modal analysis of large, sparse but unstructured symmetric matrices, Proceedings of the 17th IEEE Conference on Decision and Control, Jan. 10–12, 1979, San Diego, Calif., 45–53.
Jane Cullum and Ralph A. Willoughby (1979), Lanczos and the computation in specified intervals of the spectrum of large, sparse real symmetric matrices, eds. I. Duff and G. W. Stewart, Proceedings of the Symposium on Sparse Matrix Computations, Nov. 2–3, 1978, Knoxville, Tenn., SIAM, Philadelphia, Pa.
Jane Cullum and Ralph A. Willoughby (1978), The Lanczos tridigonalization and the conjugate gradient algorithms with local É›-orthogonality of the Lanczos vectors, RC 7152, IBM Research, Yorktown Heights, N.Y. (submitted to J. Linear Algebra).
C. C. Paige (1971), The computation of eigenvalues and eigenvectors of very large sparse matrices, Ph.D Thesis, University of London.
C. C. Paige (1972), Computational variants of the Lanczos method for the eigenproblem, J. Inst. Math., Appl. 10, 373–381.
C. C. Paige (1976), Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix, J. Inst. Math. Appl., 18, 341–349.
Jane Cullum and Ralph A. Willoughby (1979), Computing eigenvalues of large, symmetric matrices — an implementation of a Lanczos algorithm without reorthogonalization, IBM Research Report, IBM Research, Yorktown Heights, N.Y., to appear.
C. C. Paige and M. A. Saunders (1975), Solution of sparse indefinite systems of linear equations, SIAM J. Numer. Anal., 12, 617–619.
S. Kirkpatrick (1978), private communication, IBM Research, Yorktown Heights, N.Y.
T. Kaplan and L. J. Gray (1976), Elementary excitations in random substitutional alloys, Phys. Rev. B, 14, 3462–3470.
B. N Parlett (1978), A new look at the Lanczos algorithm for solving symmetric systems of linear equations, A.E.R.E. Report CSS 64, Harwell, Oxfordshire, England.
B. N. Parlett and D. S. Scott (1979), The Lanczos algorithm with selective orthogonalization, Math. Comp. 33, 217–238.
EISPAK Guide (1976), Matrix Eigensystem Routines, Lecture Notes in Computer Science, 16, B. T. Smith et al, 2nd ed. Springer-Verlag, New York.
Jane Cullum and R.A. Willoughby (1979), Computing eigenvectors (and eigenvalues) of large symmetric matrices using Lanczos tridiagonalization, IBM Research Report, RC 7718, IBM Research, Yorktown Heights, N.Y.
Daniel B. Szyld and Olof B. Widlund (1979), Applications of conjugate gradient type methods to eigenvalue calculations, to appear.
G. Peters and J. H. Wilkinson (1971), The calculation of specified eigenvectors by inverse iteration, Handbook for Automatic Computation, Vol. II Linear Algebra, ed. J. H. Wilkinson-C. Reinsch, Springer-Verlag, New York, 418–439.
Alan Jennings (1977), Matrix Computation for Engineers and Scientists, John Wiley and Sons, New York, 279–288.
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Cullum, J., Willoughby, R.A. (1980). Computing eigenvectors (and eigenvalues) of large, symmetric matrices using Lanczos tridiagonalization. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094163
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DOI: https://doi.org/10.1007/BFb0094163
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