메뉴 건너뛰기




Volumn 4699 LNCS, Issue , 2007, Pages 90-99

Sparse matrix algebra for quantum modeling of large systems

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; MATHEMATICAL MODELS; PURIFICATION; QUANTUM THEORY;

EID: 38049013979     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-75755-9_11     Document Type: Conference Paper
Times cited : (9)

References (23)
  • 1
    • 38049024267 scopus 로고    scopus 로고
    • Kittel, C: 8. In: Introduction to Solid State Physics, 7th edn., John Wiley&Sons, Chichester (1996)
    • Kittel, C: 8. In: Introduction to Solid State Physics, 7th edn., John Wiley&Sons, Chichester (1996)
  • 2
    • 2542427703 scopus 로고
    • Die gegenwartige situation in der quantenmechanik
    • Schrödinger, E.: Die gegenwartige situation in der quantenmechanik. Naturwissenschaften 23, 807 (1935)
    • (1935) Naturwissenschaften , vol.23 , pp. 807
    • Schrödinger, E.1
  • 3
    • 0001421753 scopus 로고
    • The present situation in quantum mechanics: A translation of Schrödinger's "cat paradox". Proc. Am. Phil. Soc
    • Schrödinger, E.: The present situation in quantum mechanics: a translation of Schrödinger's "cat paradox". Proc. Am. Phil. Soc. 124, 323 (1980)
    • (1980) , vol.124 , pp. 323
    • Schrödinger, E.1
  • 5
    • 0033246389 scopus 로고    scopus 로고
    • Linear scaling electronic structure methods
    • Goedecker, S.: Linear scaling electronic structure methods. Rev. Mod. Phys. 71, 1085 (1999)
    • (1999) Rev. Mod. Phys , vol.71 , pp. 1085
    • Goedecker, S.1
  • 6
    • 0001514496 scopus 로고    scopus 로고
    • A simplified density matrix minimization for linear scaling self-consistent field theory
    • Challacombe, M.: A simplified density matrix minimization for linear scaling self-consistent field theory. J. Chem. Phys. 110, 2332 (1999)
    • (1999) J. Chem. Phys , vol.110 , pp. 2332
    • Challacombe, M.1
  • 7
    • 0037961619 scopus 로고    scopus 로고
    • Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations
    • Shao, Y., Saravanan, C., Head-Gordon, M., White, C.A.: Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations. J. Chem. Phys. 118, 6144 (2003)
    • (2003) J. Chem. Phys , vol.118 , pp. 6144
    • Shao, Y.1    Saravanan, C.2    Head-Gordon, M.3    White, C.A.4
  • 8
    • 0001241557 scopus 로고    scopus 로고
    • Canonical purification of the density matrix in electronic structure theory
    • Palser, A.H.R., Manolopoulos, D.E.: Canonical purification of the density matrix in electronic structure theory. Phys. Rev. B 58, 12704 (1998)
    • (1998) Phys. Rev. B , vol.58 , pp. 12704
    • Palser, A.H.R.1    Manolopoulos, D.E.2
  • 9
    • 0037109945 scopus 로고    scopus 로고
    • Expansion algorithm for the density matrix
    • Niklasson, A.M.N.: Expansion algorithm for the density matrix. Phys. Rev. B 66, 155115 (2002)
    • (2002) Phys. Rev. B , vol.66 , pp. 155115
    • Niklasson, A.M.N.1
  • 10
    • 0037863744 scopus 로고    scopus 로고
    • Trace resetting density matrix purification in O(N) self-consistent-field theory
    • Niklasson, A.M.N., Tymczak, C.J., Challacombe, M.: Trace resetting density matrix purification in O(N) self-consistent-field theory. J. Chem. Phys. 118, 8611 (2003)
    • (2003) J. Chem. Phys , vol.118 , pp. 8611
    • Niklasson, A.M.N.1    Tymczak, C.J.2    Challacombe, M.3
  • 11
    • 1442354768 scopus 로고    scopus 로고
    • Towards idempotent reduced density matrices via particle-hole duality: McWeeny's purification and beyond
    • Mazziotti, D.A.: Towards idempotent reduced density matrices via particle-hole duality: McWeeny's purification and beyond. Phys. Rev. E 68, 66701 (2003)
    • (2003) Phys. Rev. E , vol.68 , pp. 66701
    • Mazziotti, D.A.1
  • 12
    • 0000098854 scopus 로고    scopus 로고
    • Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations
    • Holas, A.: Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations. Chem. Phys. Lett. 340, 552 (2001)
    • (2001) Chem. Phys. Lett , vol.340 , pp. 552
    • Holas, A.1
  • 13
    • 5244240756 scopus 로고    scopus 로고
    • Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations
    • Millam, J.M., Scuseria, G.E.: Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations. J. Chem. Phys. 106, 5569 (1997)
    • (1997) J. Chem. Phys , vol.106 , pp. 5569
    • Millam, J.M.1    Scuseria, G.E.2
  • 15
    • 27844477884 scopus 로고    scopus 로고
    • Systematic sparse matrix error control for linear scaling electronic structure calculations
    • Rubensson, E.H., Sałek, P.: Systematic sparse matrix error control for linear scaling electronic structure calculations. J. Comp. Chem. 26, 1628-1637 (2005)
    • (2005) J. Comp. Chem , vol.26 , pp. 1628-1637
    • Rubensson, E.H.1    Sałek, P.2
  • 16
    • 4243617877 scopus 로고    scopus 로고
    • Locality and Sparsity of Ab Initio One-Particle Density Matrices and Localized Orbitals
    • Maslen, P.E., Ochsenfeld, C., White, C.A., Lee, M.S., Head-Gordon, M.: Locality and Sparsity of Ab Initio One-Particle Density Matrices and Localized Orbitals. J. Phys. Chem. A 102, 2215 (1998)
    • (1998) J. Phys. Chem. A , vol.102 , pp. 2215
    • Maslen, P.E.1    Ochsenfeld, C.2    White, C.A.3    Lee, M.S.4    Head-Gordon, M.5
  • 17
    • 0018011681 scopus 로고
    • Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition
    • Gustavsson, F.G.: Two Fast Algorithms for Sparse Matrices: Multiplication and Permuted Transposition. ACM Trans. Math. Softw. 4, 250 (1978)
    • (1978) ACM Trans. Math. Softw , vol.4 , pp. 250
    • Gustavsson, F.G.1
  • 18
    • 0037447290 scopus 로고    scopus 로고
    • Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks
    • Saravanan, C., Shao, Y., Baer, R., Ross, P.N., Head-Gordon, M.: Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks. J. Comp. Chem. 24, 618 (2003)
    • (2003) J. Comp. Chem , vol.24 , pp. 618
    • Saravanan, C.1    Shao, Y.2    Baer, R.3    Ross, P.N.4    Head-Gordon, M.5
  • 19
    • 38049092272 scopus 로고    scopus 로고
    • Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., Sorensen, D.: LAPACK Users' Guide, release 2.0 SIAM, Philadelphia (1994)
    • Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., Sorensen, D.: LAPACK Users' Guide, release 2.0 SIAM, Philadelphia (1994)
  • 20
    • 13244279577 scopus 로고    scopus 로고
    • Minimizing development and maintenance costs in supporting persistently optimized BLAS
    • Whaley, R.C., Petitet, A.: Minimizing development and maintenance costs in supporting persistently optimized BLAS. Softw. Pract. Exper. 35, 101 (2005)
    • (2005) Softw. Pract. Exper , vol.35 , pp. 101
    • Whaley, R.C.1    Petitet, A.2
  • 21
    • 35949007371 scopus 로고
    • Density-matrix electronic-structure method with linear system-size scaling
    • Li, X.-P., Nunes, R.W., Vanderbilt, D.: Density-matrix electronic-structure method with linear system-size scaling. Phys. Rev. B 47, 10891 (1993)
    • (1993) Phys. Rev. B , vol.47 , pp. 10891
    • Li, X.-P.1    Nunes, R.W.2    Vanderbilt, D.3
  • 22
    • 0034625292 scopus 로고    scopus 로고
    • A general parallel sparse-blocked matrix multiply for linear scaling SCF theory
    • Challacombe, M.: A general parallel sparse-blocked matrix multiply for linear scaling SCF theory. Comp. Phys. Comm. 128, 93 (2000)
    • (2000) Comp. Phys. Comm , vol.128 , pp. 93
    • Challacombe, M.1
  • 23
    • 1842832833 scopus 로고    scopus 로고
    • Recursive blocked algorithms and hybrid data structures for dense matrix library software
    • Elmroth, E., Gustavson, F., Jonsson, I., Kågström, B.: Recursive blocked algorithms and hybrid data structures for dense matrix library software. SIAM Rev. 46, 3 (2004)
    • (2004) SIAM Rev , vol.46 , pp. 3
    • Elmroth, E.1    Gustavson, F.2    Jonsson, I.3    Kågström, B.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.