A Reverse Communication Interface for “Matrix-free” Preconditioned Iterative Solvers

Abstract

This paper describes an interface for a set of “matrix-free” preconditioned iterative routines for solving a sparse linear system Ax = b. These routines are matrix-free in the sense that only dense linear algebra operations are performed internally. By using reverse communication, all sparse linear algebra operations, i. e., those that depend on the matrix A or preconditioners for A, are computed outside these routines. Thus, these routines can be used regardless of the representation of A since only the action of A on a given vector is needed.

Along with its description, we also discuss the advantages and disadvantages of this interface and demonstrate its use by providing an example. A brief comparison with other common interfaces is also given.