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

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Abstract

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: Schilders' factorization, lower trapezoidal, digraph, incidence matrix, nilpotent.
Original languageEnglish
Pages (from-to)227-239
JournalNumerical Algebra, Control and Optimization
Volume4
Issue number3
DOIs
Publication statusPublished - 2014

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