An improved interval linearization for solving nonlinear problems

Numerical Algorithms

Volumn 37, Issue 1-4 SPEC. ISS., 2004, Pages 213-224

  Kolev, Lubomir V ^a  

^a TECHNICAL UNIVERSITY OF SOFIA   (Bulgaria)

Author keywords

global solution; interval linearization; interval methods; nonlinear problems

Indexed keywords

EID: 10044254740     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000049468.03595.4c     Document Type: Conference Paper

References (16)

1. I. Braems, M. Kieffer and E. Walter, Set estimation, computation of volumes and data safety, in: Scientific Computing, Validated Numerics, eds. W. Kramer and J. Wolff von Gudenberg (Kluwer Academic/Plenum, New York, 2001) pp. 267-278.
2. K. Bühler and W. Barth, A new intersection algorithm for parametric surfaces based on linear interval estimations, in: Scientific Computing, Validated Numerics, eds. W. Kramer and J. Wolff von Gudenberg (Kluwer Academic/Plenum, New York, 2001) pp. 179-190.
3. J.L.D. Comba and J. Stolfi, Affine arithmetic and its applications to computer graphics, in: Proc. of VI SIBGRAPHI (Brasilian Symposium on Computer Graphics and Image Processing), 1990, pp. 9-18.
4. E.R. Hansen, A Generalised Interval Arithmetic, Lecture Notes in Computer Science (Springer, New York, 1989) pp. 75-82.
5. E. Hansen, Global Optimization Using Interval Analysis (Marcel Dekker, New York, 1992).
6. L. Kolev, Use of interval slopes for the irrational part of factorable functions, Reliable Comput. 3 (1997) 83-93.
7. L. Kolev, An efficient interval method for global analysis of nonlinear resistive circuits, Internat. J. Circuit Theory Appl. 26 (1998) 81-92.
8. L. Kolev, A new method for global solution of systems of nonlinear equations, Reliable Comput. 4 (1998) 1-21.
9. L. Kolev, An improved method for global solution of nonlinear systems, Reliable Comput. 5(2) (1999) 103-111.
10. L. Kolev, A new interval approach to global optimization, Comput. Math. Math. Phys. 39(5) (1999) 727-737.
11. L. Kolev, Automatic computation of a linear interval enclosure, Reliable Comput. 7 (2001) 17-28.
12. L. Kolev and V. Mladenov, A linear programming implementation of an interval method for global nonlinear DC analysis, in: IEEE Internat. Conf. Electronics, Circuits and Systems. Surfing the Waves of Science and Technology, Vol. 1, Instituto Superior Tecnico Lisboa, Portugal, 7-10 September 1998, pp. 75-78.
13. R. Krawczuk and A. Neumaier, Interval slopes for rational functions and associated centred forms, SIAM J. Numer. Anal. 22 (1985) 604-616.
14. I. Nenov and D. Fylstra, Interval methods for accelerated global search in the microsoft exel solver, in: Extended Abstracts of Validated Computing 2002, ed. R.B. Kearfott, Toronto, Canada, 23-25 May 2002, pp. 145-147.
15. H. Ratschek and J. Rokne, Experiment using interval analysis for solving a circuit design problem, J. Global Optim. 3 (1993) 546-551.
16. S. Zuhe and M. A. Wolfe, On interval enclosures using slope arithmetic, Appl. Math. Comput. 39 (1990) 89-105.