A general CDC formulation for specializing the cell exclusion algorithms of finding all zeros of vector functions

Applied Mathematics and Computation

Volumn 86, Issue 2-3, 1997, Pages 235-259

  Xu, Zong Ben ^a   Zhang, Jiang She ^a   Leung, Yiu Wing ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000226754     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(96)00191-9     Document Type: Article

References (16)

1. Z. B. Xu, J. S. Zhang and W. Wang, A cell exclusion algorithm for determining all the solutions of a nonlinear system of equations, Appl. Math. & Comput. (accepted for publication).
2. J. S. Zhang, Z. Y. You and Z. B. Xu, A cell method for finding all solutions of nonlinear equations and optimization problems, Mathematica Numerica Sinica, 16, 195-203 (1994).
3. J. S. Zhang, W. Wang and B. L. Chen, A cell exclusion algorithm for finding all global minimizers of functions in multiple variables, Mathematical Numerica Sinica, Vol. 17, 443-455 (1995).
4. G. Alefeld and J. Herzberger, Introduction to Interval Computations, Academic Press, New York, London, 1983.
5. K. N. Brown, Computer-oriented algorithms for solving system of simultaneous nonlinear algebraic equations. In: Numerical Solutions of Systems of Algebraic Equations. (G. D. Byrne and C. A. Hall, Eds.), Academic Press, New York, 1973.
6. C. B. Garcia and W. I. Zangwill, Pathways to Solutions, Fixed Points, and Equilibria, Prentice-Hall, Englewood Cliffs, NJ, 1981.
7. M. W. Hirsch and S. Smale, On algorithms for solving f(x) = 0, Comm. Pure Appl. Math. 32, 281-312 (1979).
8. C. S. Hsu, Cell-to-Cell Mapping: A Method of Global Analysis of Nonlinear Systems, Springer-Verlag, New York, 1987.
9. C. S. Hsu and R. S. Guttalu, Index evaluation for dynamical systems and its application to locating all the zeros of a vector function, J. Appl. Mech. 50, 858-862 (1993).
10. C. S. Hsu and W. H. Zhu, A simplicial mapping method for locating the zeros of a function, Quart Appl. Math. 42, 41-59 (1984).
11. A. Morgan, Solving Polynomial Systems using Continuation for Engineering and Scientific Problems, Prentice-Hall, Englewood Cliffs, NJ, 1987.
12. R. E. Moore, Methods and Applications of Interval Analysis, SIAM Philadelphia, 1979.
13. J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
14. P. J. Zufiria and R. S. Guttalu, On an application of dynamical systems theory to determining all the zeros of a vector functions, J. Math. Anal. Appl., 152, 269-295 (1990).
15. P. J. Zufiria and R. S. Guttalu, A computational method for finding all the roots of a vector function, Appl. Math. & Comput. 35(1):13-59 (1990).
16. E. L. Allgower and K. Georg, Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations, SIAM Review, 22, 28-85 (1986).