Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Ortí, Robert A. van de Geijn  Home/Search
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Abstract: In this paper we present a systematic approach to the derivation of families of high-performance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is given. The paper is structured so that it can be used as a tutorial for novices. However, the method has been shown to yield new, high-performance algorithms for well-studied linear algebra operations and should also be of... (Update)
Context of citations to this paper: More
...of the triangular Sylvester equation can be derived using the methodology. The third paper focused primarily on the derivation method [5]. In particular, that paper contains a step by step recipe that novice and veteran alike can use to rapidly derive correct algorithms. In...
.... high performance linear algebra library community the bene ts of the formal derivation of algorithms in a series of previous papers [8, 12, 4]. While there we alluded at an API that allows code to re ect algorithms that have been derived to be correct, in this paper we...
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FLAME@lab: A Farewell to Indices - Bientinesi, Quintana-Ortí, al. (2003) (Correct)
Representing Linear Algebra Algorithms in Code: The FLAME API - Geijn (2003) (Correct)
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0.6: A Systematic Approach to the Design and Analysis of Linear.. - Gunnels (Correct)
0.4: Formal Linear Algebra Methods Environment (FLAME) Overview - Gunnels, Geijn, Henry (Correct)
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0.3: Formal Derivation of Algorithms: The Triangular Sylvester.. - Quintana-Ortí, Geijn (2001) (Correct)
0.3: PLAPACK: Parallel Linear Algebra Libraries Design.. - Alpatov, Baker.. (Correct)
0.3: Fault-Tolerant High-Performance Matrix Multiplication - Gunnels, Katz (2001) (Correct)
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2: FLAME: Formal linear algebra methods environment (context) - Gunnels, Henry et al. - 2001
2: A Set of Level 3 Basic Linear Algebra Subprograms (context) - Dongarra, DuCroz et al. - 1989
2: An Extended Set of Fortran Basic Linear Algebra Subprograms - Dongarra, DuCroz et al. - 1988
BibTeX entry: (Update)
Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Ort i, and Robert A. van de Geijn. The science of deriving dense linear algebra algorithms. ACM Trans. Math. Soft. submitted. http://citeseer.ist.psu.edu/article/bientinesi02science.html More
@misc{ bientinesi-science,
author = "Paolo Bientinesi and John A. Gunnels and Margaret E. Myers and Enrique
S. Quintana-Ort\'i and Robert A. van de Geijn",
title = "The Science of Deriving Dense Linear Algebra Algorithms",
url = "citeseer.ist.psu.edu/article/bientinesi02science.html" }
Citations (may not include all citations):652 A discipline of programming (context) - Dijkstra - 1976
650 An axiomatic basis for computer programming (context) - Hoare - 1969
387 A set of level 3 basic linear algebra subprograms (context) - Dongarra, Croz et al. - 1990
345 Basic linear algebra subprograms for Fortran usage (context) - Lawson, Hanson et al. - 1979
245 An extended set of FORTRAN basic linear algebra subprograms - Dongarra, Croz et al. - 1988
223 Assigning meanings to programs (context) - Floyd - 1967
157 Automatically tuned linear algebra software - Whaley, Dongarra - 1998
99 Society for Industrial and Applied Mathematics (context) - Higham, Stability et al. - 2002
29 The Science of Programming (context) - Gries - 1981
17 A Logical Approach to Discrete Math (context) - Gries, Schneider - 1992
12 A constructive approach to the problem of program correctnes.. (context) - Dijkstra - 1968
10 Flame: Formal linear algebra methods environment (context) - Gunnels, Gustavson et al. - 2001
6 A note on parallel matrix inversion (context) - Quintana, Quintana et al. - 2001
6 Formal methods for high-performance linear algebra libraries - Gunnels, Geijn - 2001
6 A family of high-performance matrix multiplication algorithm.. (context) - Gunnels, Henry et al. - 2001
4 Developing linear algebra algorithms: A collection of class .. (context) - Gunnels, Geijn - 2001
4 A Systematic Approach to the Design and Analysis of Parallel.. (context) - Gunnels - 2001
3 Developing linear algebra algorithms: Class projects Spring (context) - Bientinesi, Geijn - 2002
1 The science of programming high-performance linear algebra l.. - Bientinesi, Gunnels et al. - 2002
1 Formal derivation of algorithms for the triangular Sylvester.. (context) - Quintana-Ort, Geijn
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