Kronecker-product approximations for some function-related matrices

A new approximation tool such as sums of Kronecker products is recently found to provide a superb compression property on a series of numerical examples of quite a general nature. The purpose of the paper is explanation of this phenomenon in the form of "existence theorems" for matrix approximations of low Kronecker rank for some classes of function-related matrices including important specimens from potential theory. This lays the grounds for development of new approximation algorithms, for example, in the cases when a matrix is associated with a shift-invariant function on the Cartesian product of nonunform grids, which is of great practical interest in the solution of integral equations on plates or screens. (C) 2003 Elsevier Inc. All rights reserved.