TY - JOUR

T1 - Sparse inverse incidence matrices for Schilders' factorization applied to resistor network modeling

AU - Lungten, S.

AU - Schilders, W.H.A.

AU - Maubach, J.M.L.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.3934/naco.2014.4.227

DO - 10.3934/naco.2014.4.227

M3 - Article

VL - 4

SP - 227

EP - 239

JO - Numerical Algebra, Control and Optimization

JF - Numerical Algebra, Control and Optimization

SN - 2155-3297

IS - 3

ER -