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Efficient detection of Hessian matrix sparsity pattern. (English) Zbl 1365.65120

MSC:

65F50 Computational methods for sparse matrices
05C15 Coloring of graphs and hypergraphs
68P05 Data structures

Software:

DSJM; ADOL-C
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Full Text: DOI

References:

[1] ADMAT, http://www.cayugaresearch.com (accessed May 15, 2016).
[2] R. G. Carter. Fast Numerical Determination of Symmetric Sparsity Patterns. Tech. report MCS- P326–0992, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 1992.
[3] T. F. Coleman and J. J. Moré. Estimation of sparse Jacobian matrices and graph coloring problems.SIAM J. Numer. Anal.,20(1):187–209, 1983. · Zbl 0527.65033 · doi:10.1137/0720013
[4] A. R. Curtis, M. J. D. Powell, and J. K. Reid. On the estimation of sparse Jacobian matrices.J. Inst. Math. Appl.,13:117–119, 1974. · Zbl 0273.65036 · doi:10.1093/imamat/13.1.117
[5] The Matrix Market Project. http://math.nist.gov/MatrixMarket/ (accessed May 15, 2016).
[6] A. H. Gebremedhin, F. Manne, and A. Pothen. What Color is your Jacobian? Graph Coloring for Computing Derivatives.SIAM Rev.,47(4):629–705, 2005. · Zbl 1076.05034 · doi:10.1137/S0036144504444711
[7] A. Griewank and C. Mitev. Detecting Jacobian sparsity patterns by Bayesian probing.Math. Prog.,93(1):1–25, 2002. · Zbl 1012.65040 · doi:10.1007/s101070100281
[8] M. Hasan, S. Hossain, A. I. Khan, N. H. Mithila, and A. H. Suny. DSJM: A Software Toolkit for Direct Determination of Sparse Jacobian Matrices. To appear in the Springer Lecture Notes in Computer Science LNCS 9725, ICMS 2016, Berlin. · Zbl 1435.65043
[9] S. A. Forth. An Efficient Overloaded Implementation of Forward Mode Automatic Differentiation in MATLAB.ACM Transactions on Mathematical Software,32(2):195–222, 2006. · Zbl 1365.65053 · doi:10.1145/1141885.1141888
[10] A. Walther and A. Griewank. Getting started with ADOL-C. In U. Naumann and O. Schenk Eds., Combinatorial Scientific Computing. Chapman-Hall CRC Computational Science, Chapter 7, 181–202, 2012. · doi:10.1201/b11644-8
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