American Institute of Mathematical Sciences

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2014, 4(3): 227-239. doi: 10.3934/naco.2014.4.227

Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling

Sangye Lungten 1, , Wil H. A. Schilders 1, and  Joseph M. L. Maubach 1,

1. 

Center for Analysis, Scientific Computing and Applications, Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands, Netherlands, Netherlands

Received  December 2013 Revised  August 2014 Published  September 2014

Schilders' factorization can be used as a basis for preconditioning indefinite linear systems which arise in many problems like least-squares, saddle-point and electronic circuit simulations. Here we consider its application to resistor network modeling. In that case the sparsity of the matrix blocks in Schilders' factorization depends on the sparsity of the inverse of a permuted incidence matrix. We introduce three different possible permutations and determine which permutation leads to the sparsest inverse of the incidence matrix. Permutation techniques are based on types of sub-digraphs of the network of an incidence matrix.
Keywords: incidence matrix, Schilders' factorization, lower trapezoidal, nilpotent., digraph.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Sangye Lungten, Wil H. A. Schilders, Joseph M. L. Maubach. Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling. Numerical Algebra, Control & Optimization, 2014, 4 (3) : 227-239. doi: 10.3934/naco.2014.4.227
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show all references

References:
[1]

2nd edition, Springer-Verlag, New York, 2012. doi: 10.1007/978-1-4614-4529-6.  Google Scholar

[2]

Hindustan Book Agency, New Delhi, Springer-Verlag, London and Dordrecht, Heidelberg, New York, 2010. doi: 10.1007/978-1-84882-981-7.  Google Scholar

[3]

3rd edition, Chapman and Hall/CRC Press, Boca Raton, London, 1996.  Google Scholar

[4]

International conference on intelligent computing and cognitive informatics, IEEE 2010. Google Scholar

[5]

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 29 (2010), 28-39. Google Scholar

[6]

Journal of Computational and Applied Mathematics, 24 (1988), 89-105. doi: 10.1016/0377-0427(88)90345-7.  Google Scholar

[7]

Linear Algebra and Applications, 431 (2009), 381-395. doi: 10.1016/j.laa.2009.02.036.  Google Scholar

[8]

R. Vandebril, M. V. Barel and N. Mastronardi, Matrix Computations and Semiseparable Matrices,, The Johns Hopkins University Press, ().   Google Scholar

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