On the algebraic properties of stochastic and interval numbers
Intervenant(s) : Svetoslav MARKOV - Académie des Sciences de Bulgarie
Abstract. :In order to control round-off and input errors in the solution of numerical problems one can use either stochastic or interval arithmetic. Stochastic numbers and intervals posses similar algebraic properties, e. g. both stochastic and interval vectors form quasivector spaces with respect to addition and multiplication by scalars. A comparative survey of known and new results with respect to the algebraic properties of stochastic and interval numbers is presented. Such theoretical results allow us to solve algebraically certain numerical problems by means of stochastic arithmetic. We then compare these results with practical applications of stochastic numbers, such as the ones provided by the CESTAC method.