A note on interpolating bases

A Note on Interpolating S aling Fun tionsStephan

A Note On Minimum Path Bases

Given an undirected graph G(V,E) and a vertex subset U ⊆ V the U -space is the vector space over GF(2) spanned by the paths with end-points in U and the cycles in G(V,E). We extend Vismara’s algorithm to the computation of the union of all minimum length bases of the U -space.

Interpolating multiwavelet bases and the sampling theorem

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar functi...

Note on (De)homogenized Gröbner Bases

By employing the (de)homogenization technique in a relatively extensive setting, this note studies in detail the relation between nonhomogeneous Gröbner bases and homogeneous Gröbner bases. As a consequence, a general principle of computing Gröbner bases (for an ideal and its homogenization ideal) by passing to homogenized generators is clarified systematically. The obtained results improve and...

A note on computing range space bases of rational matrices

We discuss computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices. The main computation is the orthogonal reduction of the system matrix pencil to a special Kronecker-like form, which allows to extract a full column rank factor, whose columns form a proper rational basis of the range space. The computation of several types ...