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Volumn 7, Issue 3, 2009, Pages 755-777

Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems

Author keywords

Diagonal extraction; Electronic structure calculation; Hierarchical Schur complement

Indexed keywords


EID: 70449396467     PISSN: 15396746     EISSN: None     Source Type: Journal    
DOI: 10.4310/cms.2009.v7.n3.a12     Document Type: Article
Times cited : (116)

References (23)
  • 1
    • 84956123907 scopus 로고
    • Towards very large-scale electronic-structure calculations
    • S. Baroni and P. Giannozzi, Towards very large-scale electronic-structure calculations, Europhys. Lett., 17, 547-552, 1992.
    • (1992) Europhys. Lett , vol.17 , pp. 547-552
    • Baroni, S.1    Giannozzi, P.2
  • 3
    • 84990610636 scopus 로고
    • Fast wavelet transforms and numerical algorithms I
    • G. Beylkin, R. Coifman, and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math, 44, 141-183, 1991.
    • (1991) Comm. Pure Appl. Math , vol.44 , pp. 141-183
    • Beylkin, G.1    Coifman, R.2    Rokhlin, V.3
  • 4
    • 0003019969 scopus 로고    scopus 로고
    • Fast spectral projection algorithms for density-matrix computations
    • G. Beylkin, N. Coult, and M.J. Mohlenkamp, Fast spectral projection algorithms for density-matrix computations, J. Comput. Phys., 152, 32-54, 1999.
    • (1999) J. Comput. Phys , vol.152 , pp. 32-54
    • Beylkin, G.1    Coult, N.2    Mohlenkamp, M.J.3
  • 6
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31, 333-390, 1977.
    • (1977) Math. Comp , vol.31 , pp. 333-390
    • Brandt, A.1
  • 7
    • 47249102908 scopus 로고    scopus 로고
    • An efficient and accurate decomposition of the Fermi operator
    • M. Ceriotti, T.D. Kühne, and M. Parrinello, An efficient and accurate decomposition of the Fermi operator, J. Chem. Phys, 129, 024707, 2008.
    • (2008) J. Chem. Phys , vol.129 , pp. 024707
    • Ceriotti, M.1    Kühne, T.D.2    Parrinello, M.3
  • 8
    • 36048990421 scopus 로고    scopus 로고
    • Superfast multifrontal method for structured linear systems of equations
    • preprint
    • S. Chandrasekaran, M. Gu, X. S. Li, and J. Xia, Superfast multifrontal method for structured linear systems of equations, preprint, 2007.
    • (2007)
    • Chandrasekaran, S.1    Gu, M.2    Li, X.S.3    Xia, J.4
  • 10
    • 0020822138 scopus 로고
    • The multifrontal solution of indefinite sparse symmetric linear equations
    • J.S. Duff and J.K. Reid, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Software, 9, 302-325, 1983.
    • (1983) ACM Trans. Math. Software , vol.9 , pp. 302-325
    • Duff, J.S.1    Reid, J.K.2
  • 11
    • 0000264382 scopus 로고
    • Nested dissection of a regular finite element mesh
    • J. A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal., 10, 345-363, 1973.
    • (1973) SIAM J. Numer. Anal , vol.10 , pp. 345-363
    • George, J.A.1
  • 12
    • 0033246389 scopus 로고    scopus 로고
    • Linear scaling electronic structure methods
    • S. Goedecker, Linear scaling electronic structure methods, Rev. Mod. Phys., 71, 1085-1123, 1999.
    • (1999) Rev. Mod. Phys , vol.71 , pp. 1085-1123
    • Goedecker, S.1
  • 13
    • 0000396658 scopus 로고
    • A fast algorithm for particle simulations
    • L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Comput. Phys., 73, 325-348, 1987.
    • (1987) J. Comput. Phys , vol.73 , pp. 325-348
    • Greengard, L.1    Rokhlin, V.2
  • 14
    • 0032637646 scopus 로고    scopus 로고
    • A sparse matrix arithmetic based on Η-matrices. Part I: Introduction to Η-matrices
    • W. Hackbusch, A sparse matrix arithmetic based on Η-matrices. Part I: Introduction to Η-matrices., Computing, 62, 89-108, 1999.
    • (1999) Computing , vol.62 , pp. 89-108
    • Hackbusch, W.1
  • 15
  • 16
    • 28344457072 scopus 로고    scopus 로고
    • Stochastic linear scaling for metals and nonmetals
    • F.R. Krajewski and M. Parrinello, Stochastic linear scaling for metals and nonmetals, Phys. Rev. B, 71, 233105, 2005.
    • (2005) Phys. Rev. B , vol.71 , pp. 233105
    • Krajewski, F.R.1    Parrinello, M.2
  • 17
    • 52749085483 scopus 로고    scopus 로고
    • Computing entries of the inverse of a sparse matrix using the FIND algorithm
    • S. Li, S. Ahmed, G. Klimeck, and E. Darve, Computing entries of the inverse of a sparse matrix using the FIND algorithm, J. Comput. Phys., 227, 9408-9427, 2008.
    • (2008) J. Comput. Phys , vol.227 , pp. 9408-9427
    • Li, S.1    Ahmed, S.2    Klimeck, G.3    Darve, E.4
  • 18
    • 65149087920 scopus 로고    scopus 로고
    • L. Lin, J. Lu, R. Car, and W. E, Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems, Phys. Rev. B, 115133, 2009.
    • L. Lin, J. Lu, R. Car, and W. E, Multipole representation of the Fermi operator with application to the electronic structure analysis of metallic systems, Phys. Rev. B, 115133, 2009.
  • 19
    • 70449340107 scopus 로고    scopus 로고
    • Pole-based approximation of the Fermi-Dirac function
    • in press
    • L. Lin, J. Lu, L. Ying, and W. E, Pole-based approximation of the Fermi-Dirac function, Chinese Ann. Math Ser. B (in press).
    • Chinese Ann. Math Ser. B
    • Lin, L.1    Lu, J.2    Ying, L.3    E, W.4
  • 20
    • 0026840122 scopus 로고
    • The multifrontal method for sparse matrix solution: Theory and practice
    • J.W.H. Liu, The multifrontal method for sparse matrix solution: Theory and practice, SIAM Rev., 34, 82-109, 1992.
    • (1992) SIAM Rev , vol.34 , pp. 82-109
    • Liu, J.W.H.1
  • 22
    • 64949123438 scopus 로고    scopus 로고
    • A fast direct solver for a class of elliptic partial differential equations
    • P. G. Martinsson, A fast direct solver for a class of elliptic partial differential equations, J. Sci. Comp., 38, 316-330, 2009.
    • (2009) J. Sci. Comp , vol.38 , pp. 316-330
    • Martinsson, P.G.1
  • 23
    • 33846443185 scopus 로고    scopus 로고
    • Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations
    • T. Ozaki, Continued fraction representation of the Fermi-Dirac function for large-scale electronic structure calculations, Phys. Rev. B, 75, 035123, 2007.
    • (2007) Phys. Rev. B , vol.75 , pp. 035123
    • Ozaki, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.