On the numerical solution to linear problems using stochastic arithmetic

Abstract

International audienceIt has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. This result allows us to solve certain practical problems with stochastic numbers and to compare algebraically obtained results with practical applications of stochastic numbers, such as the ones provided by the CESTAC method. Such comparisons give additional information related to the stochastic behavior of random roundings in the course of numerical computations. A number of original numerical experiments are presented that agree with the expected theoretical results

Stochastic Arithmetic Theory and Experiments

“…The result, the relative error, the number of significant digits and the ratio "standard deviation/ √ n" are reported in Table 1. It can be seen that the standard deviation on the sum increases as √ n. This conforms to theory [2]. • Experiment 2: Computation on inner products.…”

Stochastic Arithmetic as a Model of Granular Computing

“…The solution of a linear system with stochastic right-hand sides [24]. We shall use here the special symbol+ for the arithmetic addition over standard deviations and the special symbol * for the multiplication of standard deviations by scalars.…”