Complex interval arithmetic using polar form

Reliable Computing

Volumn 12, Issue 1, 2006, Pages 1-20

  Candau, Yves ^a   Raissi, Tarek ^a   Ramdani, Nacim ^a   Ibos, Laurent ^a  

^a UNIVERSITÉ PARIS EST CRÉTEIL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; DIGITAL ARITHMETIC; OPTIMIZATION; PROBLEM SOLVING;

COMPLEX INTERVAL; INTERVAL ARITHMETIC; POLAR INTERVALS; POLAR REPRESENTATION;

NUMBER THEORY;

EID: 29044440797     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11155-006-2966-7     Document Type: Article

References (15)

1. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.
2. Boudenne, A., Ibos, L., Ghin, E., and Candau, Y.: A Simultaneous Characterisation of Thermal Conductivity and Diffusivity of Polymer Materials by a Periodic Method, Journal of Physics D: Applied Physics 37 (1) (2004), pp. 132-139.
3. Farouki, R. T. and Pottmann, H.: Exact Minkowski Products of N Complex Disks, Reliable Computing 8 (1) (2002), pp. 43-66.
4. Hansen, E.: Global Optimisation Using Interval Analysis, Marcel Dekker, New York, 1992.
5. Havriliak, Jr., S. and Havriliak, S. J.: Dielectric and Mechanical Relaxation in Materials, Munich, Hanser, 1997.
6. Henrici, P.: Circular Arithmetic and the Determination of Polynomial Zeros, Springer Lecture Notes 228, 1971, pp. 86-92.
7. Kearfott, R. B.: Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, Netherlands, 1996.
8. Klatte, R. and Ullrich, C.: Complex Sector Arithmetic, Computing 24 (2-3) (1980), pp. 139-148.
9. Lohner, R. and Wolff von Gudenberg, J.: Complex Interval Division with Maximum Accuracy, in: Computer Arithmetic 7th Symposium, Urbana (Illinois), June 1985, pp. 332-336.
10. Moore, R. E.: Interval Analysis, Prentice Hall, Englewood Cliffs, 1966.
11. Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.
12. Nickel, K.: Arithmetic of Complex Sets, Computing 24 (1980), pp. 97-105.
13. Petkovic, M. S. and Petkovic, L. D.: Complex Interval Arithmetic and Its Applications, Wiley-VCH, Berlin, 1998.
14. Raissi, T., Ibos, L., Ramdani, N., and Candau, Y.: Guaranteed Method for the Estimation of Dielectric Relaxation Models Parameters, in: 8th IEEE International Conference on Solid Dielectrics, ICSD'2004, 5-9 July 2004, Toulouse, to appear.
15. Rokne, J. and Lancaster, P.: Complex Interval Arithmetic, ACM 14 (1971), pp. 111-112.