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TR-07-02 Applying Formal Derivation Techiques to Krylov Subspace Methods
| Content Provider | Semantic Scholar |
|---|---|
| Author | Eijkhout, Victor Bientinesi, Paolo Geijn, Robert A. Van De |
| Copyright Year | 2009 |
| 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 frequent question has been whether the methodology can be broadened to iterative methods. In this paper, we show that this is indeed the case for so-called Krylov subspace methods. Our aims with this are two-fold: first of all, we show how the FLAME paradigm can simplify the derivation of subspace methods. In view of this, the fact that we only derive the classical conjugate gradient method should be viewed as a promise for the future, rather than as a limitation of this approach. Secondly, and more importantly, our use of FLAME shows how mechanical reasoning can derive full algorithm specifications from the constraints (for instance, orthogonality conditions) on the generated results. If we tie this to ongoing research in automatic optimized code generated in FLAME, we see that this research is a necessary building block towards automatic generation of optimized library software. Thus, our application domain of iterative methods is a proof-of-concept of the formalization of algorithm design and library generation. Eijkhout et al Formal derivation of Krylov methods |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://pages.tacc.utexas.edu/~eijkhout/Articles/2008-flamekrylov.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
