Enhancement of Krylov subspace spectral methods by block Lanczos iteration

Electronic Transactions on Numerical Analysis

Volumn 31, Issue , 2008, Pages 86-109

  Lambers, James V ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Block Lanczos method; Gaussian quadrature; Heat equation; Spectral methods; Stability; Variable coefficient

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NUMERICAL METHODS; SPECTROSCOPY; STABILITY;

BLOCK LANCZOS METHOD; GAUSSIAN QUADRATURES; HEAT EQUATION; SPECTRAL METHODS; VARIABLE COEFFICIENTS;

ITERATIVE METHODS;

EID: 70450190209     PISSN: None     EISSN: 10689613     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. K. Atkinson, An Introduction to Numerical Analysis, 2nd ed., Wiley, 1989.
2. S. Basu and N. K. Bose, Matrix Stieltjes series and network models, SIAM J. Math. Anal., 14 (1983),pp. 209-222.
3. G. Dahlquist, S. C. Eisenstat, and G. H. Golub, Bounds for the error of linear systems of equations using the theory of moments, J. Math. Anal. Appl., 37 (1972), pp. 151-166.
4. G. H. Golub, Some modified matrix eigenvalue problems, SIAM Rev., 15 (1973), pp. 318-334.
5. Bounds for matrix moments, Rocky Mountain J. Math., 4 (1974), pp. 207-211.
6. G. H. Golub and G. Meurant, Matrices, Moments and Quadrature, in Proceedings of the 15th Dundee Conference, June-July 1993, D. F. Griffiths and G. A. Watson, eds., Longman Scientific & Technical, 1994.
7. Matrices, Moments and Quadrature with Applications, Princeton University Press, in press.
8. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, 1996.
9. G. H. Golub and R. Underwood, The block Lanczos method for computing eigenvalues, inMathematical Software III, J. Rice Ed., 1977, pp 361-377.
10. G. H. Golub and J. Welsch, Calculation of Gauss quadrature rules, Math. Comp., 23 (1969), 221-230.
11. P. Guidotti, J. V. Lambers, and K. Soølna, Analysis of 1-D wave propagation in inhomogeneous media, Num. Funct. Anal. Opt., 27 (2006), pp. 25-55.
12. M. Hochbruck and C. Lubich, On Krylov subspace approximations to the matrix exponential operator, SIAM J. Numer. Anal., 34 (1996), pp. 1911-1925.
13. J. V. Lambers, Derivation of high-order spectral methods for time-dependent PDE using modified moments, Electron. Trans. Numer. Anal., 28 (2008), pp. 114-135, http://etna.math.kent.edu/vol.28.2007-2008/pp114-135.dir/.
14. Implicitly defined high-order operator splittings for parabolic and hyperbolic variable-coefficient PDE using modified moments, Int. J. Computational Sci., 2 (2008), pp. 376-401.
15. Krylov Subspace Methods for Variable-Coefficient Initial-Boundary Value Problems, Ph.D. Thesis, Stanford University, SCCM Program, 2003. Available at http://sccm.stanford.edu/pub/sccm/theses/James-Lambers.pdf.
16. Krylov subspace spectral methods for the time-dependent Schrödinger equation with non-smooth potentials, submitted.
17. Krylov subspace spectral methods for variable-coefficient initial-boundary value problems, Electron. Trans. Numer. Anal., 20 (2005), pp. 212-234, http://etna.math.kent.edu/vol.20.2005/pp212-234.dir/.
18. Practical implementation of Krylov subspace spectral methods, J. Sci. Comput., 32 (2007), pp. 449-476.
19. J. Stoer and R. Burlisch, Introduction to Numerical Analysis, 2nd ed., Springer Verlag, 1983.