On Some Algebraic Properties of Stochastic Numbers
نویسندگان
چکیده
Interval arithmetic and stochastic arithmetic have been both developed for the same purpose, i. e. to control errors coming from floating point arithmetic of computers and validate the results of numerical algorithms performed on computers. Interval arithmetic delivers guaranteed bounds for numerical results but requires special analysis and algorithms. On the other hand stochastic arithmetic is a model for the Cestac method which provides confidence intervals with known probability and can be easily implemented in existing numerical softwares. This work continues our study from [1] of the algebraic properties of stochastic arithmetic based on the comparison with interval arithmetic in midpoint-radius form, and on the algebraic structures that are induced by the operations on the two sets (stochastic numbers and intervals) cf. [7]. In the present paper following similar developements of interval arithmetic we introduce spaces analogous to quasilinear spaces [5, 6].
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