An efficient algorithm for solving nonlinear equations with a minimal number of trial vectors: Applications to atomic-orbital based coupled-cluster theory

Journal of Chemical Physics

Volumn 128, Issue 20, 2008, Pages

  Ziółkowski, Marcin ^a   Weijo, Ville ^a,b   Jørgensen, Poul ^a   Olsen, Jeppe ^a  

^a AARHUS UNIVERSITY   (Denmark)

^b AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTROL NONLINEARITIES; ITERATIVE METHODS; LINEAR EQUATIONS; THREE DIMENSIONAL; VECTORS;

COUPLED-CLUSTER THEORY; ITERATIVE SUBSPACE; OPTIMAL TRIAL VECTORS;

NONLINEAR EQUATIONS;

EID: 44449135552     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2928803     Document Type: Article

References (26)

1. P. Saek, S. Høst, L. Thøgersen, P. Jørgensen, P. Manninen, J. Olsen, B. Jansík, S. Reine, F. Pawowski, E. Tellgren, T. Helgaker, and S. Coriani, J. Chem. Phys. 126, 114110 (2007).
2. A. Daniels and G. Scuseria, Phys. Chem. Chem. Phys. 2, 2173 (2000).
3. T. Helgaker, P. Jørgensen, and J. Olsen, Molecular Electronic-Structure Theory (Willey, Chichester, 2002).
4. M. R. Hestenes and E. Stiefel, J. Res. Natl. Bur. Stand. 49, 409 (1952).
5. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C++: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 2002).
6. J. R. Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain (Carnegie Mellon University, Pittsburgh, PA, 1994).
7. Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (SIAM, Philadelphia, 2003).
8. J. Pople, R. Krishnan, H. Schlegel, and J. S. Binkley, Int. J. Quantum Chem., Quantum Chem. Symp. 13, 225 (1979).
9. P. E. S. Wormer, F. Visser, and J. Paldus, J. Comput. Phys. 48, 23 (1982).
10. C. C. Paige and M. A. Saunders, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 12, 617 (1975).
11. Y. Saad and M. Schultz, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 7, 856 (1986).
12. E. Stiefel, Comment. Math. Helv. 29, 157 (1955).
13. P. Vinsome, Proc. Fourth Symposium on Reservoir Simulation, Society of Petroleum Enginers of AIME 1976 (unpublished), pp. 149-159.
14. S. C. Eisenstat, H. C. Elman, and M. H. Schultz, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 20, 345 (1983).
15. P. Pulay, Chem. Phys. Lett. 73, 393 (1980).
16. P. Pulay, J. Comput. Chem. 3, 556 (1982).
17. P. Csaszar and P. Pulay, J. Mol. Struct. 114, 31 (1984).
18. O. Farkas and H. B. Schlegel, Phys. Chem. Chem. Phys. 11, 11 (2002).
19. G. E. Scuseria, T. J. Lee, and H. F. Schaefer, Chem. Phys. Lett. 130, 236 (1986).
20. J. Olsen, in Molecular Quantum Mechanics: Analytic Gradients and Beyond, edited by, A. G. Csaszar, G. Fogarasi, H. F. Schaefer, and, P. G. Szalay, (ELTE Institute of Chemistry, Budapest, 2007), pp. 85-89.
21. V. Weijo, P. Manninen, P. Jørgensen, O. Christiansen, and J. Olsen, J. Chem. Phys. 127, 074106 (2007).
22. O. Christiansen, P. Manninen, P. Jørgensen, and J. Olsen, J. Chem. Phys. 124, 084103 (2006).
23. See EPAPS Document No. E-JCPSA6-128-054821 for induction proofs of the conjugate residual algorithm. For more information on EPAPS, see http://www.aip/pubservs/epaps.html.
24. G. Arfken, Mathematical Methods for Physicists, 3rd ed. (Academic, Orlando, Florida, 1985), pp. 731-748.
25. A. van der Sluis and H. A. van der Vorst, Numer. Math. 48, 543 (1986).
26. J. Thom, H. Dunning, J. Chem. Phys. 90, 1007 (1989).