Determining Sparse Jacobian Matrices Using Two-Sided Compression: An Algorithm and Lower Bounds

Daya R. Gaur (), Shahadat Hossain () and Anik Saha ()
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Daya R. Gaur: University of Lethbridge, Department of Mathematics and Computer Science
Shahadat Hossain: University of Lethbridge, Department of Mathematics and Computer Science
Anik Saha: University of Lethbridge, Department of Mathematics and Computer Science

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 425-434 from Springer

Abstract: Abstract We study the determination of large and sparse derivative matrices using row and column compression. This sparse matrix determination problem has rich combinatorial structure which must be exploited to effectively solve any reasonably sized problem. We present a new algorithm for computing a two-sided compression of a sparse matrix. We give new lower bounds on the number of matrix-vector products needed to determine the matrix. The effectiveness of our algorithm is demonstrated by numerical testing on a set of practical test instances drawn from the literature.

Keywords: Lower Bound; Sparse Jacobian; Matrix-vector Product (MVPs); Test Instances; Dense Submatrix (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_39

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DOI: 10.1007/978-3-319-30379-6_39

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