Validation of results of collocation methods for ODEs with the CADNA library

Alt, René; Vignes, Jean

doi:10.1016/0168-9274(96)00004-9

Cited by 18 publications

(16 citation statements)

References 14 publications

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“…According to the theory of the CES-TAC method a stochastic number and consequently each component bi of b can be represented by a k-tuple of gaussian random values with known mean value m and standard deviation s. In the CADNA software [2], [3] the method is implemented with k = 3.…”

Section: Description Of the Experimentsmentioning

confidence: 99%

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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: Description Of the Experimentsmentioning

confidence: 99%

“…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].…”

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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“…It has enabled the optimization of collocation algorithms [27] and quadrature algorithms [42,43]. It has also been used for checking the reliability of numerical methods in most fields of research in applied numerical mathematics: geology [44,45], acoustics [46], solid mechanics [47], engine combustion [48], and atomic physics [49].…”

Section: Resultsmentioning

confidence: 99%

“…Here, a very simple method to estimate the optimal step size has been presented, but more sophisticated methods have also been developed in [27].…”

Section: Approximate Methodsmentioning

confidence: 99%