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Volumn 156, Issue 2, 2008, Pages 280-288

Graph coloring in the estimation of sparse derivative matrices: Instances and applications

Author keywords

Exact coloring; Mathematical derivatives; Sparsity

Indexed keywords

COMPUTATIONAL COMPLEXITY; MATRIX ALGEBRA; MOLECULAR BIOLOGY; PROBLEM SOLVING;

EID: 37049032323     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2006.07.018     Document Type: Article
Times cited : (13)

References (24)
  • 1
    • 0018456690 scopus 로고
    • New methods to color the vertices of a graph
    • Brélaz D. New methods to color the vertices of a graph. Comm. ACM 22 4 (1979) 251-256
    • (1979) Comm. ACM , vol.22 , Issue.4 , pp. 251-256
    • Brélaz, D.1
  • 2
    • 0001272884 scopus 로고
    • The cyclic coloring problem and estimation of sparse Hessian matrices
    • Coleman T.F., and Cai J.-Y. The cyclic coloring problem and estimation of sparse Hessian matrices. SIAM J. Algebraic Discrete Methods 7 2 (1986) 221-235
    • (1986) SIAM J. Algebraic Discrete Methods , vol.7 , Issue.2 , pp. 221-235
    • Coleman, T.F.1    Cai, J.-Y.2
  • 3
    • 0000421410 scopus 로고
    • Estimation of sparse Jacobian matrices and graph coloring problems
    • Coleman T.F., and Moré J.J. Estimation of sparse Jacobian matrices and graph coloring problems. SIAM J. Numer. Anal. 20 1 (1983) 187-209
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.1 , pp. 187-209
    • Coleman, T.F.1    Moré, J.J.2
  • 4
    • 0021408208 scopus 로고
    • Estimation of sparse Hessian matrices and graph coloring problems
    • Coleman T.F., and Moré J.J. Estimation of sparse Hessian matrices and graph coloring problems. Math. Programming 28 (1984) 243-270
    • (1984) Math. Programming , vol.28 , pp. 243-270
    • Coleman, T.F.1    Moré, J.J.2
  • 5
    • 0005440938 scopus 로고    scopus 로고
    • The efficient computation of sparse Jacobian matrices using automatic differentiation
    • Coleman T.F., and Verma A. The efficient computation of sparse Jacobian matrices using automatic differentiation. SIAM J. Sci. Comput. 19 4 (1998) 1210-1233
    • (1998) SIAM J. Sci. Comput. , vol.19 , Issue.4 , pp. 1210-1233
    • Coleman, T.F.1    Verma, A.2
  • 6
    • 0034889013 scopus 로고    scopus 로고
    • Frozen development in graph coloring
    • Culberson J., and Gent I. Frozen development in graph coloring. Theoret. Comput. Sci. 265 1-2 (2001) 227-264
    • (2001) Theoret. Comput. Sci. , vol.265 , Issue.1-2 , pp. 227-264
    • Culberson, J.1    Gent, I.2
  • 8
    • 37049032760 scopus 로고    scopus 로고
    • J. Dongarra, A. Lumsdaine, R. Pozo, K. Remington, A sparse matrix library in C ++ for high performance architectures, in: Proceedings of the Second Object Oriented Numerics Conference, 1994, pp. 214-218.
  • 9
    • 37049033198 scopus 로고    scopus 로고
    • I.S. Duff, R.G. Grimes, J.G. Lewis, Users' guide for the Harwell-Boeing sparse matrix collection (Release I), Technical Report tr/pa/92/86, CERFACS, 1992.
  • 10
    • 28244465516 scopus 로고    scopus 로고
    • A.H. Gebremedhin, F. Manne, A. Pothen, What color is your Jacobian? Graph coloring for computing derivatives, SIAM Rev. 47(4) 2005 629-705.
  • 11
    • 37049005091 scopus 로고    scopus 로고
    • A.V. Gelder, Another look at graph coloring via propositional satisfiability, 2002, Computational Symposium on Graph Coloring and Generalizations, COLOR02, 7-8 September 2002, Ithaca, NY.
  • 13
    • 37049037638 scopus 로고    scopus 로고
    • A. Griewank, Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. Number 19 in Frontiers in Appl. Math. SIAM, Philadelphia, Penn., 2000.
  • 14
    • 10644238699 scopus 로고    scopus 로고
    • Detecting Jacobian sparsity patterns by Bayesian probing
    • Griewank A., and Mitev C. Detecting Jacobian sparsity patterns by Bayesian probing. Math. Prog. 93 1 (2002) 1-25
    • (2002) Math. Prog. , vol.93 , Issue.1 , pp. 1-25
    • Griewank, A.1    Mitev, C.2
  • 15
    • 0003378255 scopus 로고
    • On the unconstrained optimization of partially separable functions
    • Powell M.J.D. (Ed), Academic Press, New York
    • Griewank A., and Toint Ph.L. On the unconstrained optimization of partially separable functions. In: Powell M.J.D. (Ed). Nonlinear Optimization 1981 (1982), Academic Press, New York 301-312
    • (1982) Nonlinear Optimization 1981 , pp. 301-312
    • Griewank, A.1    Toint, Ph.L.2
  • 17
    • 37049013868 scopus 로고    scopus 로고
    • S. Hossain, T. Steihaug, Reducing the number of AD passes for computing a sparse Jacobian matrix, in: G. Corliss, C. Faure, A. Griewank, L. Hascoët, U. Naumann, (Eds.), Automatic Differentiation: From Simulation to Optimization, Computer and Information Science, Springer, New York, 2001, (chapter 31), pp. 263-270.
  • 18
    • 37049021033 scopus 로고    scopus 로고
    • S. Hossain, T. Steihaug, Graph coloring in the estimation of mathematical derivatives. pp. 9-16, 2002. Computational Symposium on Graph Coloring and Generalizations, COLOR02, 7-8 September 2002, Ithaca, NY.
  • 19
    • 37049013450 scopus 로고    scopus 로고
    • S. Hossain, T. Steihaug, Optimal direct determination of sparse Jacobian matrices, Technical Report 254, Department of Informatics, University of Bergen, Norway, October 2003. (Revised version to appear in Optimization Methods and Software).
  • 21
    • 0020765471 scopus 로고
    • Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem
    • McCormick S.T. Optimal approximation of sparse Hessians and its equivalence to a graph coloring problem. Math. Programming 26 (1983) 153-171
    • (1983) Math. Programming , vol.26 , pp. 153-171
    • McCormick, S.T.1
  • 22
    • 0031285908 scopus 로고    scopus 로고
    • Optimal sizing for a class of nonlinearly elastic materials
    • Moré J.J., and Wu J. Optimal sizing for a class of nonlinearly elastic materials. SIAM J. Optim. 7 3 (1997) 814-836
    • (1997) SIAM J. Optim. , vol.7 , Issue.3 , pp. 814-836
    • Moré, J.J.1    Wu, J.2
  • 24
    • 0005496584 scopus 로고    scopus 로고
    • Algorithmic differencing
    • Facius A., and Kulisch U. (Eds), Springer, Vienna
    • Rall L.B., and Reps T.W. Algorithmic differencing. In: Facius A., and Kulisch U. (Eds). Perspectives on Enclosure Methods (2001), Springer, Vienna
    • (2001) Perspectives on Enclosure Methods
    • Rall, L.B.1    Reps, T.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.