Stochastic Arithmetic: s-spaces and Some Applications

Markov, Svetoslav; Alt, René; Lamotte, Jean Luc

doi:10.1023/b:numa.0000049474.51465.41

Cited by 8 publications

(6 citation statements)

References 7 publications

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“…Section 3 considers the algebraic solution of linear systems of equations which right-hand sides involve stochastic numbers. In Section 4 we extend our idea from [5] to compare the algebraic solution of a problem involving stochastic numbers with the solution obtained numerically by the CESTAC method. Several numerical experiments are presented.…”

Section: Introductionmentioning

confidence: 99%

On the numerical solution to linear problems using stochastic arithmetic

Alt

Lamotte

Markov

2006

Proceedings of the 2006 ACM Symposium on Applied Computing

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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

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Section: Introductionmentioning

confidence: 99%

On the numerical solution to linear problems using stochastic arithmetic

Alt

Lamotte

Markov

2006

Proceedings of the 2006 ACM Symposium on Applied Computing

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“…Note also that 0 s −X = (0, 0) s −(m, σ) = (−m, σ), which equals −1 s * X. Many of the properties of stochastic arithmetic and stochastic numbers have been studied from the point of view of abstract algebraic structures, especially with respect to the operations addition and multiplication by scalars [1], [3], [7], [8], in particular we have:…”

Section: Stochastic Numbers and Stochastic Arithmeticmentioning

confidence: 99%

Stochastic Arithmetic Theory and Experiments

Alt¹,

Lamotte²,

Markov³

2010

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Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

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“…Table 2.3 presents the number of exact decimal digits, N , provided by CADNA in the computed determinant (25) as a function of ε, which determines the uncertainty of a 12 and a 33 .…”

Section: When This Determinant Is Computed With Ieee 754 Fp Arithmetimentioning

confidence: 99%