LP narrowing: A new strategy for finding all solutions of nonlinear equations

Applied Mathematics and Computation

Volumn 215, Issue 1, 2009, Pages 405-413

  Yamamura, Kiyotaka ^a   Suda, Koki ^a   Tamura, Naoya ^a  

^a CHUO UNIVERSITY   (Japan)

Author keywords

Dual simplex method; Finding all solutions; Interval analysis; Linear programming; Nonlinear equation

Indexed keywords

COMPUTATION TIME; DUAL SIMPLEX METHOD; EFFICIENT ALGORITHM; FINDING ALL SOLUTIONS; INTERVAL ANALYSIS; LINEAR PROGRAMMING TECHNIQUES; NEW STRATEGY; NUMERICAL EXAMPLE;

ALGORITHMS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION; NONLINEAR ANALYSIS; OPTIMIZATION; ORDINARY DIFFERENTIAL EQUATIONS;

NONLINEAR EQUATIONS;

EID: 67949094308     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.05.017     Document Type: Article

References (25)

1. Alefeld G., and Herzberger J. Introduction to Interval Computations (1983), Academic Press, New York
2. Alefeld G., and Potra F. A new class of interval methods with higher order of convergence. Computing 42 (1989) 69-80
3. Allgower E., and Georg K. Simplicial and continuation methods for approximating fixed points and solutions to systems of equations. SIAM Rev. 22 (1980) 28-85
4. Georg K. A new exclusion test. J. Comput. Appl. Math. 152 (2003) 147-160
5. Granvilliers L., and Benhamou F. RealPaver: an interval solver using constraint satisfaction techniques. ACM Trans. Math. Softw. 32 (2006) 138-156
6. Hansen E.R., and Sengupta S. Bounding solutions of systems of equations using interval analysis. BIT 21 (1981) 203-211
7. Jaulin L., Kieffer M., Didrit O., and Walter E. Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics (2001), Springer, London
8. Kearfott R.B. Interval arithmetic techniques in the computational solution of nonlinear systems of equations: introduction, examples, and comparisons. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics vol. 26 (1990), American Mathematical Society, Providence, RI 337-357
9. In: Kearfott R.B., and Kreinovich V. (Eds). Applications of Interval Computations (1996), Kluwer Academic Publishers, Dordrecht
10. Krawczyk R. Newton-algorithmen zur bestimmung von nullstellen mit fehlerschranken. Computing 4 (1969) 187-201
11. Lebbah Y., Michel C., Rueher M., Daney D., and Merlet J.-P. Efficient and safe global constraints for handling numerical constraint systems. SIAM J. Numer. Anal. 42 (2005) 2076-2097
12. Miyajima S., and Kashiwagi M. Existence test for solution of nonlinear systems applying affine arithmetic. J. Comput. Appl. Math. 199 (2007) 304-309
13. Moore R.E. Methods and Applications of Interval Analysis (1979), SIAM Studies in Applied Mathematics, Philadelphia
14. Moré J.J. A collection of nonlinear model problems. In: Allgower E.L., and Georg K. (Eds). Computational Solution of Nonlinear Systems of Equations. Lectures in Applied Mathematics vol. 26 (1990), American Mathematical Society, Providence, RI 723-762
15. Neumaier A. Interval Methods for Systems of Equations (1990), Cambridge University Press, Cambridge, England
16. Syam M.I. Nonlinear optimization exclusion tests for finding all solutions of nonlinear equations. Appl. Math. Comput. 170 (2005) 1104-1116
17. Wolfe M.A. A modification of Krawczyk's algorithm. SIAM J. Numer. Anal. 17 (1980) 376-379
18. Wolfe M.A. On bounding solutions of underdetermined systems. Reliab. Comput. 7 (2001) 195-207
19. Xu Z.-B., Zhang J.S., and Wang W. A cell exclusion algorithm for determining all the solutions of a nonlinear system of equations. Appl. Math. Comput. 80 (1996) 181-208
20. Yamamura K. An algorithm for representing functions of many variables by superpositions of functions of one variable and addition. IEEE Trans. Circuits Syst. I 43 (1996) 338-340
21. Yamamura K. Finding all solutions of nonlinear equations using linear combinations of functions. Reliab. Comput. 6 (2000) 105-113
22. Yamamura K., Kawata H., and Tokue A. Interval solution of nonlinear equations using linear programming. BIT 38 (1998) 186-199
23. Yamamura K., and Tanaka S. Finding all solutions of systems of nonlinear equations using the dual simplex method. BIT 42 (2002) 214-230
24. Yamamura K., and Fujioka T. Finding all solutions of nonlinear equations using the dual simplex method. J. Comput. Appl. Math. 152 (2003) 587-595
25. Chvátal V. Linear Programming (1983), W.H. Freeman Company, New York p. 158