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Nowadays, parallel computing is ubiquitous in several application fields,both in engineering and science. The computations rely on the floating-pointarithmetic specified by the IEEE754 Standard. In this context, an elementarybrick of computation, used everywhere, is the sum of a sequence of numbers.This sum is subject to many numerical errors in floating-point arithmetic. Toalleviate this issue, we have introduced a new parallel algorithm for summing asequence of floating-point numbers. This algorithm which scales up easily withthe number of processors, adds numbers of the same exponents first. In thisarticle, our main contribution is an extensive analysis of its efficiency withrespect to several properties: accuracy, convergence and reproducibility. Inorder to show the usefulness of our algorithm, we have chosen a set ofrepresentative numerical methods which are Simpson, Jacobi, LU factorizationand the Iterated power method.

An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods