On monotonicity of the Lanczos approximation to the matrix exponential

Linear Algebra and Its Applications

Volumn 429, Issue 7, 2008, Pages 1679-1683

  Druskin, Vladimir ^a  

^a SCHLUMBERGER DOLL RESEARCH   (United States)

Author keywords

Krylov subspace; Matrix exponential; Strictly monotonic convergence; Symmetric matrix; Total positivity

Indexed keywords

POLYNOMIAL APPROXIMATION;

APPROXIMATE SOLUTIONS; KRYLOV SUBSPACES; LANCZOS; MATRIX EXPONENTIAL; MONOTONICALLY; MONOTONICITY; SYMMETRIC MATRICES;

MATRIX ALGEBRA;

EID: 48749087049     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2008.04.046     Document Type: Article

References (12)

1. Druskin V., Greenbaum A., and Knizhnerman L. Using nonorthogonal Lanczos vectors in the computation of matrix functions. SIAM J. Sci. Comput. 19 (1998) 38-54
2. Druskin V., and Knizhnerman L. A spectral semi-discrete method for the numerical solution of three-dimensional non-stationary electrical prospecting problems. Izv. AN USSR, ser. "Physics of Solid Earth" 8 (1988) 63-74 (in Russian; translated into English)
3. Druskin V., and Knizhnerman L. Two polynomial methods of calculating functions of symmetric matrices. USSR Comput. Math. Math. Phys. 29 (1989) 112-121
4. Frommer A., and Simoncini V. Matrix functions. In: Schilders W., and van der Vorst H. (Eds). Model Order Reduction: Theory, Research Aspects and Applications, Mathematics in Industry (2008), Springer, Heidelberg
5. Gallopulos E., and Saad Y. Efficient solution of parabolic equations by Krylov approximation method. SIAM J. Sci. Stat. Comput. 13 (1992) 1236-1264
6. Hochbruck M., and Lubich C. On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34 (1997) 1911-1925
7. Nour-Omid B. Lanczos method for heat conduction analysis. Internat. J. Numer. Meth. Eng. 24 1 (1987) 251-262
8. Karlin S. Total Positivity (1968), Stanford University Press
9. Parlett B. The Symmetric Eigenvalue Problem (1998), SIAM
10. Tal-Ezer H. Spectral methods in time for parabolic problems. SIAM J. Numer. Anal. 26 1 (1989) 1-11
11. Van der Vorst H. An iterative solution method for solving f (A) x = b using Krylov subspace information obtained for the symmetric positive definite matrix. J. Comput. Appl. Math. 18 2 (1987) 249-263
12. Saad Y. Numerical Methods for Large Eigenvalue Problems (1992), Manchester University Press