Towards mechanical derivation of Krylov solver libraries

Abstract

In a series of papers, it has been shown that algorithms for dense linear algebra operations can be systematically and even mechanically derived from the mathematical specification of the operation. A framework named FLAME (Formal Linear Algebra Methods Environment) has been developed to realize this aim. The goals of this paper are two-fold: first, we show how the approach can be used to derive a nonsymmetric CG algorithm, which provides strong evidence that the approach applies to Krylov subspace methods in general. Secondly, and more importantly, we show that the reasoning can be made sufficiently systematic that mechanical derivation is within reach. Thus this research shows a promise for providing necessary building blocks towards automatic generation of library software for iterative methods for solving linear systems. Eijkhout et al Mechanical Derivation