On the solution to numerical problems using stochastic arithmetic

12th GAMM - IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, SCAN 2006, Conference Post-Proceedings

Volumn , Issue , 2006, Pages 6-13

  Alt, René ^a   Lamotte, Jean Luc ^a   Markov, Svetoslav ^b  

^a CNRS   (France)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATION THEORY; NUMERICAL METHODS;

ALGEBRAIC PROPERTIES; ALGEBRAIC THEORIES; ARITHMETIC OPERATIONS; AXIOMATIC APPROACH; LAGRANGE POLYNOMIALS; NUMERICAL PROBLEMS; STOCHASTIC ARITHMETIC; STOCHASTIC NUMBERS;

STOCHASTIC SYSTEMS;

EID: 47849117632     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SCAN.2006.35     Document Type: Conference Paper

References (12)

1. Alt, R., S. Markov, On the Algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic, In: W. Kraemer and J. Wolff v. Gudenberg (Eds.), Scientific Computing, Validated Numerics, Interval Methods, Kluwer, 2001, 331-342.
2. Alt, R., J.-L. Lamotte, S. Markov, Abstract structures in stochastic arithmetic, In: B. Bouchon-Meunier, R. R. Yager (Eds.), Proc. 11-th Conference on Information Processing and Management of Uncertainties in Knowledge-based Systems (IPMU 2006), Editions EDK, Paris, 2006, 794-801.
3. Alt, R., J. Vignes, Validation of Results of Collocation Methods for ODEs with the CADNA Library. Appl. Numer. Math. 20 (1996), 1-21.
4. Chesneaux, J. M., J. Vignes, Les fondements de l'arithmétique stochastique, C.R. Acad. Sci., Paris, Sér. I, Math. 315 (1992), 1435-1440.
5. INTLAB - INTerval LABoratory Version 5.2., www.ti3.tu-harburg.de/ rump/intlab/
6. Markov, S., R. Alt, Stochastic arithmetic: Addition and Multiplication by Scalars, Appl. Numer. Math. 50 (2004), 475-488.
7. Markov, S., R. Alt, J.-L. Lamotte, Stochastic Arithmetic: S-spaces and Some Applications, Numer. Algorithms 37 (1-4), 275-284, 2004.
8. Vignes, J., R. Alt, An Efficient Stochastic Method for Round-Off Error Analysis, in: Accurate Scientific Computations, LNCS 235, Springer, 1985, 183-205.
9. Vignes, J., Review on Stochastic Approach to Round-Off Error Analysis and its Applications. Math. and Comp. in Sim. 30, 6 (1988), 481-491.
10. Vignes, J., A Stochastic Arithmetic for Reliable Scientific Computation, Math. and Comp. in Sim. 35 (1993), 233-261.
11. Yao, Y. Y., Granular Computing: basic issues and possible solutions, In: P. P. Wang (Ed.), Proc. of the 5-th Joint Conference on Information Sciences, Vol. I, Atlantic City, New Jersey, USA, February 27-March 3, 2000, Association for Intelligent Machinery, 186-189.
12. http://www.lip6.fr/cadna