Complex Interval Arithmetic Using Polar Form

Abstract : In this paper, the polar representation of complex numbers is extended to complex polar intervals or sectors; detailed algorithms are derived for performing basic arithmetic operations on sectors. While multiplication and division are exactly defined, addition and subtraction are not, and we seek to minimize the pessimism introduced by these operations. Addition is studied as an optimization problem which is analytically solved. The complex interval arithmetic thus defined is illustrated with some numerical examples which show that in many applications, the polar representation is more advisable.
Type de document :
Article dans une revue
Reliable Computing, Springer Verlag, 2006, 20 (1), pp.1-20
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https://hal.archives-ouvertes.fr/hal-00161338
Contributeur : Tarek Raïssi <>
Soumis le : mardi 10 juillet 2007 - 14:57:10
Dernière modification le : jeudi 11 janvier 2018 - 06:21:07

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  • HAL Id : hal-00161338, version 1

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Yves Candau, Tarek Raissi, Nacim Ramdani, Laurent Ibos. Complex Interval Arithmetic Using Polar Form. Reliable Computing, Springer Verlag, 2006, 20 (1), pp.1-20. 〈hal-00161338〉

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