Application of the three-way decomposition for matrix compression

We present a new method to compress and invert 3D integral operators on rectangular non-regular grids. This method requires a small amount of memory to store the compressed matrix and in most cases can provide a good preconditioner for the solution of linear systems with this matrix. We demonstrate efficiency of this method for the solution of some model discrete problems associated with integral(R)(3) A((x) over bar, (y) over bar )f((x) over bar )d((x) over bar) = u((y) over bar), (x) over bar, (y) over bar is an element of R-3 where A((x) over bar, (y) over bar) such as 1/\(x) over bar - (y) over bar vertical bar is considered on a non-regular grid. The arithmetical complexity of matrix-vector and preconditioner-vector multiplications are about N-4/3 operations and there are only about N-2/3 words of memory to store. Copyright (C) 2002 John Wiley Sons, Ltd.