https://hal-enac.archives-ouvertes.fr/hal-03664170Benmouhoub, FarahFarahBenmouhoubUPVD - Université de Perpignan Via DomitiaGaroche, Pierre-LoïcPierre-LoïcGarocheENAC - Ecole Nationale de l'Aviation CivileMartel, MatthieuMatthieuMartelUPVD - Université de Perpignan Via DomitiaAn Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical MethodsHAL CCSD2022floating-point arithmeticaccurate summationnumerical accuracynumerical methodsconvergencereproducibility[INFO.INFO-CL] Computer Science [cs]/Computation and Language [cs.CL][INFO.INFO-SE] Computer Science [cs]/Software Engineering [cs.SE][INFO.INFO-FL] Computer Science [cs]/Formal Languages and Automata Theory [cs.FL]Garoche, Pierre-Loïc - Analyses formelles et exhaustives de systèmes embarqués de contrôle à base de calculs intensifs - - FEANICSES2017 - ANR-17-CE25-0018 - AAPG2017 - VALID - 2022-05-10 18:26:482022-05-12 03:40:242022-05-11 10:32:22enConference papershttps://hal-enac.archives-ouvertes.fr/hal-03664170/document10.1007/978-3-030-95561-8_10application/pdf1Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.