Robust mixing for ab initio quantum mechanical calculations

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 7, 2008, Pages

  Marks, L D ^a   Luke, D R ^b  

^a Northwestern University   (United States)

^b UNIVERSITY OF DELAWARE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50049090380     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.075114     Document Type: Article

References (48)

1. W. Kohn and L. J. Sham, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.140. A1133 140, A1133 (1965).
2. N. D. Mermin, Phys. Rev. PRVAAH 0096-8250 10.1103/PhysRev.137.A1441 137, A1441 (1965).
3. E. Prodan, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/25/004 38, 5647 (2005).
4. distinguishes a definition from an equation.
5. P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Institute for Materials Chemistry, Technical University of Vienna, Vienna, 2006).
6. F. Crittin and M. Bierlaire, Proceedings of the Third Swiss Transport Research Conference (STRC), 2003 (unpublished).
7. D. D. Johnson, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.12807 38, 12807 (1988).
8. M. Kawata, C. M. Cortis, and R. A. Friesner, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.475854 108, 4426 (1998).
9. P. Pulay, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/0009-2614(80)80396-4 73, 393 (1980).
10. G. P. Srivastava, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/17/6/002 17, L317 (1984).
11. D. Vanderbilt and S. G. Louie, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.30.6118 30, 6118 (1984).
12. D. Singh, H. Krakauer, and C. S. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.8391 34, 8391 (1986).
13. S. Boyd and L. Vandenberghe, Convex Optimization (Oxford University Press, New York, 2003).
14. C. G. Broyden, Math. Comput. MCMPAF 0025-5718 10.2307/2003941 19, 577 (1965).
15. R. H. Byrd, J. Nocedal, and R. B. Schnabel, Math. Program. MHPGA4 0025-5610 10.1007/BF01582063 63, 129 (1994).
16. J. E. Dennis and J. J. Moré, SIAM Rev. SIREAD 0036-1445 10.1137/1019005 19, 46 (1977).
17. The Frobenious norm of a matrix is the square root of the sum of squares of the matrix entries.
18. C. M. IP and M. J. Todd, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAAM 0036-1429 10.1137/0725015 25, 206 (1988).
19. P. Wolfe, Commun. ACM CACMA2 0001-0782 10.1145/368518.368542 2 (12), 12 (1959).
20. J. G. P. Barnes, Comput. J. CMPJA6 0010-4620 8, 66 (1965).
21. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic, New York, 1970).
22. W. Gragg and G. Stewart, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. SJNAAM 0036-1429 10.1137/0713070 13, 889 (1976).
23. D. M. Gay and R. B. Schnabel, in Nonlinear Programming, edited by, O. L. Mangasarian,,, R. R. Meyer,, and, S. M. Robinson, (Academic, New York, 1978), Vol. 3, pp. 245-281.
24. J. M. Martínez, BIT, Nord. Tidskr. Inf.behandl. NBITAB 0006-3835 10.1007/BF01930854 19, 236 (1979).
25. R. B. Schnabel, University of Colorado Technical Report No. CU-CS-247-83, 1983 (unpublished).
26. J. E. Dennis and R. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1996).
27. J. Ford and I. Moghrabi, J. Comput. Appl. Math. JCAMDI 0377-0427 10.1016/S0377-0427(97)00075-7 82, 105 (1997).
28. H. Fang and Y. Saad, University of Minnesota Technical Report, 2007 (unpublished).
29. D. R. Luke, J. V. Burke, and R. G. Lyon, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450139075 44, 169 (2002).
30. J. M. Borwein and A. S. Lewis, Convex Analysis and Nonlinear Optimization: Theory and Examples, 2nd ed. (Springer-Verlag, New York, 2006).
31. F. E. Browder, Proc. Natl. Acad. Sci. U.S.A. 54, 1041 (1965). 0027-8424
32. W. A. Kirk, Am. Math. Monthly AMMYAE 10.2307/2313345 72, 1004 (1965).
33. J. B. Baillon, R. E. Bruck, and S. Reich, Houst. J. Math HJMADZ 0362-1588 4, 1 (1978).
34. G. Pratt, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.88.1217 88, 1217 (1952).
35. E. Prodan and P. Nordlander, J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1022810601639 111, 967 (2003).
36. A projection is defined as any mapping P such that P2 =P. An orthogonal projection onto a set C is the point in C that is nearest, with respect to the norm, to the point being projected.
37. K. Levenberg, Q. Appl. Math. 2, 164 (1944). 0033-569X
38. D. Marquardt, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0111030 11, 431 (1963).
39. A. N. Tihonov, Dokl. Akad. Nauk SSSR 151, 501 (1963). 0002-3264
40. A. N. Tihonov, Dokl. Akad. Nauk SSSR 153, 49 (1963). 0002-3264
41. P. C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (SIAM, Philadelphia, 1998).
42. A. E. Hoerl and R. W. Kennard, Technometrics TCMTA2 0040-1706 10.2307/1267351 12, 55 (1970).
43. J. J. Moreau, Acad. Sci., Paris, C. R. COREAF 0001-4036 255, 2897 (1962).
44. D. Raczkowski, A. Canning, and L. W. Wang, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.121101 64, 121101 (R) (2001).
45. K. M. Ho, J. Ihm, and J. D. Joannopoulos, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.25.4260 25, 4260 (1982).
46. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.3865 77, 3865 (1996).
47. R. Laskowski and P. Blaha, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/20/6/064207 20, 064207 (2008).
48. D. R. Luke, SIAM J. Optim. SJOPE8 1052-6234 10.1137/070681399 19, 714 (2008).