Electronic states in the Anderson model of localization: Benchmarking eigenvalue algorithms

Computer Physics Communications

Volumn 121, Issue , 1999, Pages 517-523

  Schreiber, Michael ^a   Milde, Frank ^a   Römer, Rudolf A ^a  

^a CHEMNITZ UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; EIGENVALUES AND EIGENFUNCTIONS; FRACTALS; MATHEMATICAL MODELS; MATRIX ALGEBRA;

ANDERSON MODEL; LANCZOS METHOD; MULTIFRACTAL ANALYSIS; WAVEFUNCTIONS;

BAND STRUCTURE;

EID: 0033185175     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0010-4655(99)00396-3     Document Type: Article

References (28)

1. P.W. Anderson, Phys. Rev. 109 (1958) 1492.
2. J.G.L. Booten, H.A. Van der Vorst, P.M. Meijer, H.J.J. te Riele, Technical Report CWI-NM-R9414, Centrum voor Wiskunde en Informatica, Amsterdam, July 1994.
3. I.A. Cavers, SIAM J. Matrix Anal. Appl. 15 (1994) 1363.
4. A.B. Chhabra, R.V. Jensen, Phys. Rev. Lett. 62 (1989) 1327.
5. J. Cullum, R.A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations (Birkhäuser, Boston, 1985). http://www.netlib.org/lanczos/.
6. J. Demmel, J. Gilbert, X. Li, SuperLU Users' Guide, 1997. http://www.netlib.org/scalapack/prototype/superlu_ug.ps.
7. U. Elsner, V. Mehrmann, F. Milde, R.A. Römer, M. Schreiber, SIAM J. Sci. Comp., in print.
8. R. Fletcher, in: Proc. Dundee Biennal Conf. Numerical Analysis 1974, G. Watson (Ed.) (Springer, Heidelberg, 1975) p. 73.
9. R. Freund, N. Nachtigal, QMRPACK. http://www.netlib. org/linalg/.
10. R. Freund, N. Nachtigal, Numer. Math. 60 (1991) 315.
11. G.H. Golub, C.F.v. Loan, Matrix Computations (John Hopkins University Press, Baltimore, 3rd ed., 1996).
12. H. Grussbach, M. Schreiber, Phys. Rev. B 57 (1995) 663.
13. H. Grussbach, M. Schreiber, Chem. Phys. 178 (1993) 733.
14. Harwell Subroutine Library, http://www.dci.clrc.ac.uk/ Activity.asp?HSL.
15. E. Hofstetter, M. Schreiber, Phys. Rev. B 48 (1993) 16979.
16. R.B. Lehoucq, J.A. Scott, Technical Report MCS-P547-1195, Argonne National Laboratory, Argonne, 1996. ftp://info. mcs.anl.gov/pub/tech_reports/reports/P547.ps.Z. submitted to ACM Trans. Math. Software.
17. R.B. Lehoucq, D. Sorensen, C. Yang, ARPACK USERS GUIDE: Solution of Large Scale Eigenvalue Problems by Implicitly Restarted Arnoldi Methods (SIAM, 1998).
18. F. Milde, R.A. Römer, M. Schreiber, Phys. Rev. B 55 (1997) 9463.
19. Y. Saad, Numerical Methods for Large Eigenvalue Problems: Theory and Algorithms (Wiley, New York, 1992).
20. M. Schreiber, Physica A 167 (1990) 188.
21. M. Schreiber, H. Grussbach, Phys. Rev. Lett. 67 (1991) 607.
22. D.E. Stewart, Z. Leyk, Meschach. http://www.netlib.org/c /meschach/.
23. P. Sonneveld, SIAM J. Sci. Statist. Comput. 12 (1989) 36.
24. D. Sorensen, C. Sun, private communications.
25. Y. Saad, M. Schultz, SIAM J. Sci. Statist. Comput. 7 (1986) 856.
26. H.A. Van der Vorst, SIAM J. Sci. Statist. Comput. 12 (1992) 613.
27. F. Wegner, Nucl. Phys. B 316 (1989) 663.
28. I.K. Zharekeshev, B. Kramer, Phys. Rev. Lett. 79 (1997) 717.