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 ∫ A ( x̄ , ȳ ) f ( x̄ )d x̄ = u ( ȳ ), x̄ , ȳ ϵℝ 3 , where A ( x̄ , ȳ ) such as 1/∣ x̄ − ȳ ∣ 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.