Superlinear convergence rates for the Lanczos method applied to elliptic operators

Numerische Mathematik

Volumn 77, Issue 4, 1997, Pages 487-499

  Hanke, Martin ^a,b  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039972002     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050297     Document Type: Article

References (13)

1. Brown, J.D., Chu, M.T., Ellison, D.C., Plemmons, R.J. (eds.) (1994), Proceedings of the Cornelius Lanczos International Centenary Conference, SIAM, Philadelphia
2. Chihara, T.S. (1978) An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, London, Paris
3. Cullum, J.K., Willoughby, R.A. (1985) Lanczos Algorithms for Large Symmetric Eigenvalue Computations. Vol. I Theory, Birkhäuser, Boston, Basel, Stuttgart
4. Ericsson, T., Ruhe, A. (1980) The spectral transformation Lanczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems, Math. Comp. 35, 1251-1268
5. Golub, G.H., Van Loan, C.F. (1989) Matrix Computations, The Johns Hopkins University Press, Baltimore
6. Grosjean, C.C. (1984) The orthogonality property of the Lommel polynomials and a twofold infinity of relations between Rayleigh's σ-sums, J. Comp. Appl. Math. 10, 355-382
7. Hackbusch, W. (1985) Multi-Grid Methods and Applications, Springer-Verlag, Berlin, Heidelberg, New York
8. Lanczos, C. (1950) An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. National Bureau Standards 45, 255-282
9. Nevanlinna, O. (1993) Convergence of Iterations for Linear Equations, Birkhäuser Verlag, Basel, Boston, Berlin
10. Parlett, B.N. (1980) The Symmetric Eigenvalue Problem, Prentice Hall, Inc., Englewood Cliffs, N.J.
11. Szegö, G. (1975) Orthogonal Polynomials, Amer. Math. Soc. Colloqu. Publ., Vol. 23, Amer. Math. Soc., Providence, Rhode Island
12. Watson, G.N. (1966) A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge
13. Weinberger, H.F. (1974) Variational Methods for Eigenvalue Approximation, SIAM, Philadelphia