Abstract
In this paper we present a set of linear algebra subroutines which serve as building blocks for numerical software, and develop algorithms to implement these subroutines as a portable library for parallel computers. We consider these routines as a part of the standard arithmetic of a computer Therefore they have to deliver a validated result of high accuracy
Abstract
Представлен набор линейно-алгебраических подпрограмм, которые могут служить строительными бдоками для чисденного программного обеспечення, а также алгоритмы для реализанин зтнх подпрограмм в впде переносимой библиотеки для паралдельных комньюгеров. Зти пропедуры рассматриваются как часть стандартной арифметики компьютера, позтому они должны возврашать проверенный резвльгат высокой точности.
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Albrecht, R., Alefeld, G., and Stetter, H. J. (eds)Validation numerics. Computing Suppl.9 (1993).
Bohlender, G. and Wolff von Gudenberg, J.Accurate matrix multiplication on the array processor AMT-DAP. In: Kaucher, E., Markov, S. M., and Mayer, G. (eds) “Computer Arithmetic, Scientific Computation and Mathematical Modelling,” IMACS Annals on Computing and Applied Mathematics12 (1992).
Cordes, D. and Kaucher, E.Self-validating computation for sparse matrix problems. In: Kaucher, E., Kulisch, U., and Ullrich, C. (eds) “Computerarithmetic,” Teubner, Stuttgart, 1987.
Kulisch, U., and Miranker, W. L.The arithmetic of the digital computer: a new approach. SIAM Review28 (1) (March 1986).
Philipsen, M. and Tichy, W.Compiling for massively parallel machines. In: “Proc. of Code-Generation-Concepts, Tools, Techniques”, Springer Series on Workshops in Computing, 1992.
Reith, R.Wissenschaftliches Rechnen auf Multicomputern — BLAS-Routinen und die Lösung linearer Gleichungssysteme mit Fehlerkontrolle. Dissertation, Universität Basel, 1993.
Rump, S. M.Validated solution of large linear systems. In: [1].Validation numerics. Computing Suppl.9 (1993).
Wolff von Gudenberg, JModelling SIMD — type parallel arithmetic operations in Ada. In: Christodoulakis, D. (ed.) “Ada: The Choice for '92”, LNCS 499, Springer Berlin, 1991.
Wolff von Gudenberg, JAccurate matrix operations on hypercube computers. In: Herzberger, J. and Atanassova, L. (eds) “Computer Arithmetic and Enclosure Methods,” North-Holland, Amsterdam, 1992.
Wolff von Gudenberg, J.Implementation of accurate matrix multiplication on the CM-2. In: [1]Validation numerics. Computing Suppl.9 (1993).
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von Gudenberg, J.W. Parallel accurate linear algebra subroutines. Reliable Comput 1, 189–199 (1995). https://doi.org/10.1007/BF02384054
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DOI: https://doi.org/10.1007/BF02384054