On the numerical solution to linear problems using stochastic arithmetic

摘要

It 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.