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Volumn 28, Issue 6, 2013, Pages 1218-1232

Optimal direct determination of sparse Jacobian matrices

Author keywords

graph colouring; independent set; Jacobian matrix; row partitioning

Indexed keywords

AUTOMATIC DIFFERENTIATIONS; COMPUTATIONAL RESULTS; DIRECT DETERMINATION; FINITE DIFFERENCING; GRAPH COLOURING; INDEPENDENT SET; INDEPENDENT VARIABLES; ROW PARTITIONING;

EID: 84886298156     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2012.693927     Document Type: Article
Times cited : (9)

References (31)
  • 1
    • 0001580287 scopus 로고
    • Computing large sparse jacobian matrices using automatic differentiation
    • B.M.Averick, J.J. Moré, C.H. Bischof, A. Carle, and A. Griewank, Computing large sparse Jacobian matrices using automatic differentiation, SIAM J. Sci. Comput. 15(2) (1994), pp. 285-294
    • (1994) SIAM J. Sci. Comput , vol.15 , Issue.2 , pp. 285-294
    • Averick, B.M.1    Moré, J.J.2    Bischof, C.H.3    Carle, A.4    Griewank, A.5
  • 2
    • 0035450053 scopus 로고    scopus 로고
    • Inexact quasi-newton methods for sparse systems of nonlinear equations
    • L. Bergamaschi, I. Moret, and G. Zilli, Inexact Quasi-Newton methods for sparse systems of nonlinear equations, Future Gener. Comp. Syst. 18(1) (2001), pp. 41-53
    • (2001) Future Gener. Comp. Syst , vol.18 , Issue.1 , pp. 41-53
    • Bergamaschi, L.1    Moret, I.2    Zilli, G.3
  • 3
    • 0018456690 scopus 로고
    • New methods to color the vertices of a graph
    • D. Brélaz, New methods to color the vertices of a graph, Commun. ACM 22(4) (1979), pp. 251-256
    • (1979) Commun. ACM , vol.22 , Issue.4 , pp. 251-256
    • Brélaz, D.1
  • 4
    • 0040027656 scopus 로고
    • Large sparse numerical optimization
    • Springer Verlag, Berlin
    • T.F. Coleman, Large Sparse Numerical Optimization, Lecture Notes in Computer Science,Vol. 165, Springer-Verlag, Berlin, 1984
    • (1984) Lecture Notes in Computer Science , vol.165
    • Coleman, T.F.1
  • 5
    • 0001272884 scopus 로고
    • The cyclic coloring problem and estimation of sparse hessian matrices
    • T.F. Coleman and J-Y. Cai, The cyclic coloring problem and estimation of sparse Hessian matrices, SIAM J. Alg. Disc. Meth. 7(2) (1986), pp. 221-235
    • (1986) SIAM J. Alg. Disc. Meth , vol.7 , Issue.2 , pp. 221-235
    • Coleman, T.F.1    Cai, J.-Y.2
  • 6
    • 0000421410 scopus 로고
    • Estimation of sparse jacobian matrices and graph coloring problems
    • T.F. Coleman and J.J. Moré, Estimation of sparse Jacobian matrices and graph coloring problems, SIAM J. Numer. Anal. 20(1) (1983), pp. 187-209
    • (1983) SIAM J. Numer. Anal , vol.20 , Issue.1 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 7
    • 0021408208 scopus 로고
    • Estimation of sparse hessian matrices and graph coloring problems
    • T.F. Coleman and J.J. Moré, Estimation of sparse Hessian matrices and graph coloring problems, Math. Prog. 28(1984), pp. 243-270
    • (1984) Math. Prog , vol.28 , pp. 243-270
    • Coleman, T.F.1    Moré, J.J.2
  • 8
    • 0005440938 scopus 로고    scopus 로고
    • The efficient computation of sparse jacobian matrices using automatic differentiation
    • T.F. Coleman and A. Verma, The efficient computation of sparse Jacobian matrices using automatic differentiation, SIAM J. Sci. Comput. 19(4) (1998), pp. 1210-1233
    • (1998) SIAM J. Sci. Comput , vol.19 , Issue.4 , pp. 1210-1233
    • Coleman, T.F.1    Verma, A.2
  • 10
  • 11
    • 0022769785 scopus 로고
    • On the successive projections approach to least-squares problems
    • J.E. Dennis, Jr and T. Steihaug, On the successive projections approach to least-squares problems, SIAM J. Numer. Anal. 23(4) (1986), pp. 717-733
    • (1986) SIAM J. Numer. Anal , vol.23 , Issue.4 , pp. 717-733
    • Dennis Jr., J.E.1    Steihaug, T.2
  • 13
    • 0004236492 scopus 로고    scopus 로고
    • 3rd ed., Johns Hopkins University Press, Baltimore, MD
    • G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd ed., Johns Hopkins University Press, Baltimore, MD, 1996
    • (1996) Matrix Computations
    • Golub, G.H.1    Van Loan, C.F.2
  • 14
    • 0001911625 scopus 로고
    • Some bounds on the complexity of gradients, jacobians, and Hessians
    • P.M. Pardalos, ed.,World Scientific Publishers, River Edge, NJ
    • A. Griewank, Some bounds on the complexity of gradients, Jacobians, and Hessians, in Complexity in Numerical Optimization, P.M. Pardalos, ed.,World Scientific Publishers, River Edge, NJ, 1993, pp. 128-162
    • (1993) Complexity in Numerical Optimization , pp. 128-162
    • Griewank, A.1
  • 15
    • 10644238699 scopus 로고    scopus 로고
    • Detecting jacobian sparsity patterns by bayesian probing
    • A. Griewank and C. Mitev, Detecting Jacobian sparsity patterns by Bayesian probing, Math. Prog. 93(1) (2002), pp. 1-25
    • (2002) Math. Prog , vol.93 , Issue.1
    • Griewank, A.1    Mitev, C.2
  • 17
    • 84866975150 scopus 로고    scopus 로고
    • Evaluating derivatives principles and techniques of algorithmic differentiation
    • 2nd ed Philadelphia, PA, USA
    • A. Griewank and A.Walther, Evaluating Derivatives, Principles and Techniques of Algorithmic Differentiation, 2nd ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2008
    • (2008) Society for Industrial and Applied Mathematics
    • Griewank, A.1    Walther, A.2
  • 18
    • 76249125631 scopus 로고    scopus 로고
    • CsegGraph: A graph colouring instance generator
    • S. Hossain, CsegGraph: A graph colouring instance generator, Int. J. Comput. Math. 86(10-11) (2009), pp. 1956-1967
    • (2009) Int. J. Comput. Math , vol.86 , Issue.10-11 , pp. 1956-1967
    • Hossain, S.1
  • 19
    • 0032292043 scopus 로고    scopus 로고
    • Computing a sparse jacobian matrix by rows and columns optim
    • A.S. Hossain and T. Steihaug, Computing a sparse Jacobian matrix by rows and columns, Optim. Meth. Software 10 (1998), pp. 33-48
    • (1998) Meth. Software , vol.10 , pp. 33-48
    • Hossain, A.S.1    Steihaug, T.2
  • 20
    • 28244464920 scopus 로고    scopus 로고
    • Reducing the number ofad passes for computing a sparse jacobian matrix
    • Chapter 31, G. Corliss C. Faure, A. Griewank, L. Hascoët, and U. Naumann, eds. Computer and Information Science Springer, NewYork
    • S. Hossain and T. Steihaug, Reducing the number ofAD passes for computing a sparse Jacobian matrix, inAutomatic Differentiation: From Simulation to Optimization, Chapter 31, G. Corliss, C. Faure, A. Griewank, L. Hascoët, and U. Naumann, eds., Computer and Information Science, Springer, NewYork, 2002, pp. 263-270
    • (2002) Automatic Differentiation: From Simulation to Optimization , pp. 263-270
    • Hossain, S.1    Steihaug, T.2
  • 22
    • 37049032323 scopus 로고    scopus 로고
    • Graph coloring in the estimation of sparse derivative matrices: Instances and applications
    • S. Hossain and T. Steihaug, Graph coloring in the estimation of sparse derivative matrices: Instances and applications, Discrete Appl. Math. 156(2) (2008), pp. 280-288
    • (2008) Discrete Appl. Math , vol.156 , Issue.2 , pp. 280-288
    • Hossain, S.1    Steihaug, T.2
  • 23
    • 84886243080 scopus 로고    scopus 로고
    • The CPR method and beyond: Prologue, in combinatorial scientific computing
    • U. Naumann, O. Schenk, H.D. Simon, and S. Toledo, eds. Dagstuhl, Germany. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Germany
    • S. Hossain and T. Steihaug, The CPR method and beyond: Prologue, in Combinatorial Scientific Computing, U. Naumann, O. Schenk, H.D. Simon, and S. Toledo, eds., number 09061 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Germany, 2009, 3
    • (2009) Number 09061 in Dagstuhl Seminar Proceedings , pp. 3
    • Hossain, S.1    Steihaug, T.2
  • 24
    • 34247388040 scopus 로고    scopus 로고
    • MIQR: A multilevel incomplete QR preconditioner for large sparse least-squares problems
    • N. Li andY. Saad, MIQR: A multilevel incomplete QR preconditioner for large sparse least-squares problems, SIAM J. Matrix Anal. Appl. 28(2) (2006), pp. 524-550
    • (2006) SIAM J. Matrix Anal. Appl , vol.28 , Issue.2 , pp. 524-550
    • Li, N.1    Saad, Y.2
  • 25
    • 0020765471 scopus 로고
    • Optimal approximation of sparse hessians and its equivalence to a graph coloring problem
    • S.T.McCormick, Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem, Math. Prog. 26 (1983), pp. 153-171
    • (1983) Math. Prog , vol.26 , pp. 153-171
    • McCormick, S.T.1
  • 26
    • 0031285908 scopus 로고    scopus 로고
    • Optimal sizing for a class of nonlinearly elastic materials
    • J.J. Moré and J. Wu, Optimal sizing for a class of nonlinearly elastic materials, SIAM J. Optim. 7(3) (1997), pp. 814-836
    • (1997) SIAM J. Optim , vol.7 , Issue.3 , pp. 814-836
    • Moré, J.J.1    Wu, J.2
  • 27
    • 0000147566 scopus 로고
    • Estimation of sparse Jacobian matrices
    • G.N. Newsam and J.D. Ramsdell, Estimation of sparse Jacobian matrices, SIAM J. Alg. Disc. Meth. 4(3) (1983), pp. 404-417
    • (1983) SIAM J. Alg. Disc. Meth , vol.4 , Issue.3 , pp. 404-417
    • Newsam, G.N.1    Ramsdell, J.D.2
  • 28
    • 0000495643 scopus 로고
    • On the estimation of sparse hessian matrices
    • M.J.D. Powell and P.L. Toint, On the estimation of sparse Hessian matrices, SIAM J. Numer. Anal. 16 (1979), pp. 1060-1074
    • (1979) SIAM J. Numer. Anal , vol.16 , pp. 1060-1074
    • Powell, M.J.D.1    Toint, P.L.2
  • 30
    • 0001085784 scopus 로고    scopus 로고
    • ILUM: A multi-elimination ilu preconditioner for general sparse matrices
    • Y. Saad, ILUM: A Multi-elimination ILU preconditioner for general sparse matrices, SIAM J. Sci. Comput. 17(4)(1996), pp. 830-847
    • (1996) SIAM J. Sci. Comput , vol.17 , Issue.4 , pp. 830-847
    • Saad, Y.1
  • 31
    • 37149019503 scopus 로고    scopus 로고
    • Another look at graph coloring via propositional satisfiability
    • A. Van Gelder, Another look at graph coloring via propositional satisfiability, Discrete Appl. Math. 156 (2008), pp. 230-243
    • (2008) Discrete Appl. Math , vol.156 , pp. 230-243
    • Van Gelder, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.