Rank decomposition in zero pattern matrix algebras

Harm Bart; Torsten Ehrhardt; Bernd Silbermann

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An introduction to hierarchical matrices

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We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short $ℋ$ -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector...

A basic decomposition result related to the notion of the rank of a matrix and applications.

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Moore-Penrose inverse of a hollow symmetric matrix and a predistance matrix

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By a hollow symmetric matrix we mean a symmetric matrix with zero diagonal elements. The notion contains those of predistance matrix and Euclidean distance matrix as its special cases. By a centered symmetric matrix we mean a symmetric matrix with zero row (and hence column) sums. There is a one-toone correspondence between the classes of hollow symmetric matrices and centered symmetric matrices, and thus with any hollow symmetric matrix D we may associate a centered symmetric matrix...