An efficient stochastic method for round-off error analysis

On the numerical solution to linear problems using stochastic arithmetic

“…In practice, stochastic numbers are computed using the CESTAC method, which is a Monte-Carlo method consisting in performing each arithmetic operation several times using an arithmetic with a random rounding mode, see [2], [6], [7].…”

Stochastic Arithmetic as a Model of Granular Computing

“…The CESTAC method was first developed by M. La Porte and J. Vignes [7][8][9][10][11] and was later generalized by the later in [12][13][14][15][16][17][18][19].…”

On the solution to numerical problems using stochastic arithmetic

“…The operator negation is an automorphism ¬ : S n → S n , that is: ¬(A + B) = ¬A + (¬B), and involution: ¬(¬A) = A. These properties can be checked experimentally, say, by a CESTAC-like method, see e. g. [8], [9], [10]. So, we next consider these properties as axiomatically given, and we want to derive some simple consequences.…”

“…Such an N -tuple which is a sampling of a Gaussian random variable is named in this context a discrete stochastic number. In practice the CES-TAC method has been implemented in a software called CADNA in which the N samples of the stochastic numbers are randomly rounded up or down so as to take into account the round-off errors, see [3], [8], [9], [12], with the same idea that directed rounding is used for implementing interval arithmetic [5].…”