Journal of Science of the Hiroshima University, Series A-I (Mathematics)

On Lanczos' algorithm for tri-diagonalization

Tetsuro Yamamoto

Full-text: Open access

Article information

Source
J. Sci. Hiroshima Univ. Ser. A-I Math. Volume 32, Number 2 (1968), 259-284.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
http://projecteuclid.org/euclid.hmj/1206138652

Mathematical Reviews number (MathSciNet)
MR0245193

Zentralblatt MATH identifier
0181.17202

Subjects
Primary: 65.35

Citation

Yamamoto, Tetsuro. On Lanczos' algorithm for tri-diagonalization. J. Sci. Hiroshima Univ. Ser. A-I Math. 32 (1968), no. 2, 259--284. http://projecteuclid.org/euclid.hmj/1206138652.


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References

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  • [2] Brooker, R. A. and F. H. Sumner: The method of Lanczos for calculating the characteristic roots and vectors of a real symmetric matrix, Proc. Instn elect. Engrs B., 103 (1956), Supple. 114-119.
  • [3] Causey, R. L. and R. T. Gregory: On Lanczos algorithm for tri-diagonalizing matrices, SIAM Review, 3 (1961), 322-328.
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  • [6] Householder, A. S.: The theory of matrices in numerical analysis, Blaisdell Publishing Company, 1964.
  • [7] Lanczos, G.: An iteration for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards, 45 (1950), 255-282.
  • [8] Rutishauser, H.: Beitrage zur Kentniss des Biorthogonalisierungs-Algorithmus von Lanczos, Z. Angew. Math. Physik, 4 (1953), 35-56.
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  • [10] Wilkinson, The algebraic eigenvalue problem, Clarendon Press. Oxford, 1965.
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  • [12] Yamamoto, On the eigenvalues of compact operators in a Hilbert space, Numer. Math., 11 (1968), 211- 219.