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Volumn 30, Issue 4, 2008, Pages 1302-1319

Out-of-core implementations of cholesky Factorization: Loop-based versus recursive algorithms

Author keywords

Cholesky factorization; Out of core algorithms

Indexed keywords

CHOLESKY FACTORIZATION; CHOLESKY FACTORIZATION ALGORITHM; CHOLESKY FACTORIZATIONS; COMPLEX MATRICES; INPUT/OUTPUT OPERATIONS; LINEAR ALGEBRA PACKAGE; MAIN MEMORY; NUMERICAL EXPERIMENTS; OUT-OF-CORE; OUT-OF-CORE ALGORITHMS; POSITIVE-DEFINITE MATRICES; RECURSIVE ALGORITHMS; RECURSIVE FORMULATION;

EID: 70449440599     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/06067256X     Document Type: Article
Times cited : (7)

References (26)
  • 1
    • 33749988758 scopus 로고    scopus 로고
    • A preliminary out-of-core extension of a parallel multifrontal solver
    • Springer-Verlag, New York
    • E. Agullo, A. Guermouche, and J.-Y. L'Excellent, A preliminary out-of-core extension of a parallel multifrontal solver, in Euro-Par 2006 Parallel Processing, Springer-Verlag, New York, 2006, pp. 1053-1063.
    • Euro-Par 2006 Parallel Processing , vol.2006 , pp. 1053-1063
    • Agullo, E.1    Guermouche, A.2    L'excellent, J.-Y.3
  • 3
    • 18044400448 scopus 로고    scopus 로고
    • A recursive formulation of Cholesky factorization of a matrix in packed storage
    • B. S. Andersen, J. Wasniewski, and F. G. Gustavson, A recursive formulation of Cholesky factorization of a matrix in packed storage, ACM Trans. Math. Software, 27 (2001), pp. 214-244.
    • (2001) ACM Trans. Math. Software , vol.27 , pp. 214-244
    • Andersen, B.S.1    Wasniewski, J.2    Gustavson, F.G.3
  • 5
    • 27844549797 scopus 로고    scopus 로고
    • A parallel distributed solver for large dense symmetric systems: Applications to geodesy and electromagnetism problems
    • M. Baboulin, L. Giraud, and S. Gratton, A parallel distributed solver for large dense symmetric systems: Applications to geodesy and electromagnetism problems, J. High Speed Comput., 19 (2005), pp. 353-363.
    • (2005) J. High Speed Comput. , vol.19 , pp. 353-363
    • Baboulin, M.1    Giraud, L.2    Gratton, S.3
  • 6
    • 84966239375 scopus 로고
    • Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method, Part 1: The continuous problem, Part 2: The discrete problem
    • A. Bendali, Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method, Part 1: The continuous problem, Part 2: The discrete problem, Math. Comp., 43 (1984), pp. 29-68.
    • (1984) Math. Comp. , vol.43 , pp. 29-68
    • Bendali, A.1
  • 8
    • 0038380607 scopus 로고    scopus 로고
    • A preconditioner for the electric field integral equation based on Calderon formulas
    • S. H. Christiansen and J.-C. Nédélec, A preconditioner for the electric field integral equation based on Calderon formulas, SIAM J. Numer. Anal., 40 (2002), pp. 1100-1135.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 1100-1135
    • Christiansen, S.H.1    Nédélec, J.-C.2
  • 9
    • 0942268043 scopus 로고    scopus 로고
    • Discrete Fredholm properties and convergence estimates for the electric field integral equation
    • S. H. Christiansen, Discrete Fredholm properties and convergence estimates for the electric field integral equation, Math. Comp., 73 (2004), pp. 143-167.
    • (2004) Math. Comp. , vol.73 , pp. 143-167
    • Christiansen, S.H.1
  • 10
    • 0034455094 scopus 로고    scopus 로고
    • The fast multipole method (I): Error analysis and asymptotic complexity
    • E. Darve, The fast multipole method (I): Error analysis and asymptotic complexity, SIAM J. Numer. Anal., 38 (2000), pp. 98-128.
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 98-128
    • Darve, E.1
  • 11
    • 0034487070 scopus 로고    scopus 로고
    • The design and implementation of the parallel out-ofcore ScaLAPACK LU, QR and Cholesky factorization routines
    • E. F. D'Azevedo and J. Dongarra, The design and implementation of the parallel out-ofcore ScaLAPACK LU, QR and Cholesky factorization routines, Concurrency: Practice and Experience, 12 (2000), pp. 1481-1493.
    • (2000) Concurrency: Practice and Experience , vol.12 , pp. 1481-1493
    • D'azevedo, E.F.1    Dongarra, J.2
  • 13
    • 1842832833 scopus 로고    scopus 로고
    • Recursive blocked algorithms and hybrid data structures for dense matrix library software
    • E. Elmroth, F. Gustavson, I. Jonsson, and B. Kågström, Recursive blocked algorithms and hybrid data structures for dense matrix library software, SIAM Rev., 46 (2004), pp. 3-45.
    • (2004) SIAM Rev. , vol.46 , pp. 3-45
    • Elmroth, E.1    Gustavson, F.2    Jonsson, I.3    Kågström, B.4
  • 14
    • 84860927033 scopus 로고    scopus 로고
    • Developing linear algebra algorithms: A collection of class projects
    • Department of Computer Sciences, The University of Texas, Austin, TX
    • J. A. Gunnels and R. A. van de Geijn, Developing Linear Algebra Algorithms: A Collection of Class Projects, FLAME Working Note 3, Department of Computer Sciences, The University of Texas, Austin, TX, 2001.
    • (2001) FLAME Working Note 3
    • Gunnels, J.A.1    Van De Geijn, R.A.2
  • 16
    • 0034312453 scopus 로고    scopus 로고
    • Minimal storage high performance Cholesky factorization via blocking and recursion
    • F. G. Gustavson and I. Jonsson, Minimal storage high performance Cholesky factorization via blocking and recursion, IBM J. Res. Develop., 44 (2000), pp. 823-849.
    • (2000) IBM J. Res. Develop. , vol.44 , pp. 823-849
    • Gustavson, F.G.1    Jonsson, I.2
  • 17
    • 1642372163 scopus 로고    scopus 로고
    • Parallel and fully recursive multifrontal sparse Cholesky
    • D. Irony, G. Shklarski, and S. Toledo, Parallel and fully recursive multifrontal sparse Cholesky, Future Generation Comput. Syst., 20 (2004), pp. 425-440.
    • (2004) Future Generation Comput. Syst. , vol.20 , pp. 425-440
    • Irony, D.1    Shklarski, G.2    Toledo, S.3
  • 18
    • 33745328323 scopus 로고    scopus 로고
    • Rapid development of highperformance out-of-core solvers
    • Lyngby, Denmark
    • T. Joffrain, E. S. Quintana-Ortí, and R. A. van de Geijn, Rapid development of highperformance out-of-core solvers, in PARA 2004, Lyngby, Denmark, 2004, pp. 413-422.
    • PARA 2004 , vol.2004 , pp. 413-422
    • Joffrain, T.1    Quintana-Ortí, E.S.2    Van De Geijn, R.A.3
  • 19
    • 0012415109 scopus 로고    scopus 로고
    • Acoustic and electromagnetic equations: Integral representations for harmonic problems
    • Springer-Verlag, New York
    • J.-C. Nédélec, Acoustic and electromagnetic equations: Integral representations for harmonic problems, Appl. Math. Sci. 144, Springer-Verlag, New York, 2001.
    • (2001) Appl. Math. Sci. , vol.144
    • Nédélec, J.-C.1
  • 23
    • 0031496750 scopus 로고    scopus 로고
    • Locality of reference in LU decomposition with partial pivoting
    • S. Toledo, Locality of reference in LU decomposition with partial pivoting, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 1065-1081.
    • (1997) SIAM J. Matrix Anal. Appl. , vol.18 , pp. 1065-1081
    • Toledo, S.1
  • 24
    • 0002831423 scopus 로고    scopus 로고
    • A survey of out-of-core algorithms in numerical linear algebra
    • J. Abello and J. S. Vitter, eds., American Mathematical Society Press, Providence, RI
    • S. Toledo, A survey of out-of-core algorithms in numerical linear algebra, in External Memory Algorithms and Visualization, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., J. Abello and J. S. Vitter, eds., American Mathematical Society Press, Providence, RI, 1999, pp. 161-180.
    • (1999) External Memory Algorithms and Visualization, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , pp. 161-180
    • Toledo, S.1
  • 26
    • 70449433660 scopus 로고    scopus 로고
    • Efficient Parallel Out-of-core implementation of the cholesky factorization
    • Department of Computer Sciences, The University of Texas at Austin, Austin, TX, December
    • R. Wesley, Efficient Parallel Out-of-core Implementation of the Cholesky Factorization, PLAPACK Working Note 11, Department of Computer Sciences, The University of Texas at Austin, Austin, TX, December 1999.
    • (1999) PLAPACK Working Note 11
    • Wesley, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.