Stochastic Arithmetic Theory and Experiments

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

doi:10.55630/sjc.2010.4.1-10

Cited by 7 publications

(1 citation statement)

References 6 publications

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“…The corresponding methodology for the practical application of the new structures in relation to problems analogous to so-called "dependency problems" in interval arithmetic is also given and some numerical experiments in the lines of our previous investigations, see e. g. [4], [6], [3], [7] are presented.…”

Section: Introduction Stochastic Numbers and Stochastic Arithmetic Havementioning

confidence: 99%

Quasilinear Structures in Stochastic Arithmetic and their Application

Markov¹,

Alt

Lamotte

2017

SJC

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Stochastic arithmetic has been developed as a model for computing with imprecise numbers. In this model, numbers are representedby independent Gaussian variables with known mean value and standarddeviation and are called stochastic numbers. The algebraic properties of stochastic numbers have already been studied byseveral authors. Anyhow, in most life problems the variables are not independentand a direct application of the model to estimate the standard deviation on the result of a numerical computation may lead to some overestimation of the correct value. In this work “quasilinear” algebraic structures based on standard stochastic arithmeticare studied and, from pure abstract algebraic considerations, new arithmetic operationscalled “inner stochastic addition and subtraction” are introduced. They appear to be stochastic analogues to the inner interval addition and subtractionused in interval arithmetic. The algebraic properties of these operations and the involved algebraic structures are then studied. Finally, the connection of these inner operations to the correlation coefficient ofthe variables is developed and it is shown that they allow the computation with non-independent variables. The corresponding methodology for the practicalapplication of the new structures in relation to problems analogous to “dependency problems”in interval arithmetic is given and some numerical experiments showing the interest ofthese new operations are presented.ACM Computing Classification System (1998): D.2.4, G.3, G.4.

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Section: Introduction Stochastic Numbers and Stochastic Arithmetic Havementioning

confidence: 99%

Quasilinear Structures in Stochastic Arithmetic and their Application

Markov¹,

Alt

Lamotte

2017

SJC

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Extension of frozen orbits and Sun-synchronous orbits around terrestrial planets using continuous low-thrust propulsion

Jiang

2015

Astrophys Space Sci

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Frozen orbits and Sun-synchronous orbits are useful in exploration of terrestrial planets' surface and atmosphere with a view to future human exploration. This work therefore develops novel orbits around terrestrial planets using continuous low-thrust propulsion to enable one new and unique investigations of the planets. This paper considers the use of continuous acceleration by solar electric propulsion, to achieve artificial frozen orbits and artificial Sun-synchronous orbits around terrestrial planets. These artificial orbits are similar to natural frozen orbits and Sunsynchronous orbits around Mercury, Venus, the Earth, and Mars, and the orbital parameters can be designed arbitrarily with the help of continuous low-thrust control. The control strategies to achieve the artificial orbits take into account J 2 , J 3 , and J 4 perturbations of terrestrial planets. It is proved that the control strategies minimize characteristic velocity. Relevant formulas are derived, and numerical results are presented. For the natural frozen orbits, the arguments of periapsis are about 270°for Mercury, Venus, and Mars, whereas about 90°for the Earth. By exerting both radial and transverse thrusts simulation shows that the control acceleration and characteristic velocity of the artificial frozen orbit around Mercury are the smallest among these plants. The characteristic velocity within one orbital period for Mercury is only 0.0089 m/s. The natural Sun-synchronous orbits exist around the Earth and Mars, but not around Mercury and Venus. By offsetting the perturbation acceleration in norm direction, the control acceleration and characteristic velocity of the artificial Sun-synchronous orbit around Mars are less than those of the others. The characteristic velocity

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