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.
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© 1991 Computational Mechanics Publications
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Heroux, M.A. (1991). A Reverse Communication Interface for “Matrix-free” Preconditioned Iterative Solvers. In: Brebbia, C.A., Peters, A., Howard, D. (eds) Applications of Supercomputers in Engineering II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3660-0_15
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DOI: https://doi.org/10.1007/978-94-011-3660-0_15
Publisher Name: Springer, Dordrecht
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