On the localization and computation of zeros of Bessel functions

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 77, Issue 6, 1997, Pages 467-475

  Vrahatis, M N ^a   Grapsa, T N ^a   Ragos, O ^a   Zafiropoulos, F A ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243157786     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970770615     Document Type: Article

References (28)

1. ABERTH, O.: Computation of topological degree using interval arithmetic, and applications. Math. Comput. 62 (1994), 171-178.
2. ALEXANDROFF, P.; HOPF, H.: Topologie. Springer-Verlag, Berlin 1935; reprinted: Bronx, Chelsea, New York 1965.
3. BARNETT, A. R.: KLEIN: Coulomb functions for real λ and positive energy to high accuracy. Comput. Phys. Commun. 24 (1981), 141-159.
4. BARNETT, A. R.: COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed's method. Comput. Phys. Commun. 27 (1982), 147-166.
5. COURANT, R.; HILBERT, D.: Methods of mathematical physics. Vol. 1. Wiley-Interscience, New York 1953.
6. CRONIN, J.: Fixed points and topological degree in nonlinear analysis. Mathematical Surveys No. 11, Amer. Math. Soc., Providence, Rhode Island 1964.
7. HOENDERS, B. J.; SLUMP, C. H.: On the calculation of the exact number of zeroes of a set of equations. Computing 30 (1983), 137-147.
8. HOENDERS, B. J.; SLUMP, C. H.: On the determination of the number and multiplicity of zeros of a function. Computing 47 (1992), 323-336.
9. KAVVADIAS, D.; VRAHATIS, M. N.: Locating and computing all the simple roots and extrema of a function. SIAM J. Sci. Comput. 17 (1996), 1232-1248.
10. KEARFOTT, R. B.: Computing the degree of maps and a generalized method of bisection. Ph. D. dissertation, Department of Mathematics, University of Utah, S.L.C. 1977.
11. KEARFOTT, R. B.: An efficient degree-computation method for a generalized method of bisection. Numer. Math. 32 (1979), 109-127.
12. KEARFOTT, R. B.: private communication.
13. O'NEIL, T.; THOMAS, J.: The calculation of the topological degree by quadrature. SIAM J. Numer. Anal. 12 (1975), 673-680.
14. ORTEGA, J. M.; RHEINBOLT, W. C.: Iterative solution of nonlinear equations in several variables. Academic Press, New York 1970.
15. PAPADIMITRIOU, C. H.; STEIGLITZ, K.: Combinatorial optimization: algorithms and complexity. Prentice-Hall, Inc., Englewood Cliffs, New Jersey 1982.
16. e série 8 (1892), 5-24.
17. PICARD, E. : Traité d'analyse. 3rd ed., chap. 4.7, Gauthier-Villars, Paris 1922.
18. PRESS, W. H.; TEUKOLSKY, S. A.; VETTERLING, W. T.; FLANNERY, W. T.: Numerical recipes, the art of scientific computing. 2nd ed. Cambridge University Press, New York 1992.
19. SIKORSKI, K.: Bisection is optimal. Numer. Math. 40 (1982), 111-117.
20. SIKORSKI, K.; TROJAN, G. M.: Asymptotic near optimality of the bisection method. Numer. Math. 57 (1990), 421-433.
21. SLUMP, C. H.; HOENDERS, B. J.: The determination of the location of the global maximum of a function in the presence of several local extrema. IEEE Trans. Inform. Theory IT-31 (1985), 490-497.
22. n. Numer. Math. 25 (1975), 23-38.
23. STYNES, M.: An algorithm for the numerical calculation of the degree of a mapping. Ph. D. dissertation, Department of Mathematics, Oregon State University, Corvallis 1977.
24. STYNES, M.: An algorithm for numerical calculation of topological degree. Appl. Anal. 9 (1979), 63-77.
25. VRAHATIS, M. N.: Solving systems of nonlinear equations using the nonzero value of the topological degree. ACM Trans. Math. Software 14 (1988), 312-329.
26. VRAHATIS, M. N.: CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations. ACM Trans. Math. Software 14 (1988), 330-336.
27. VRAHATIS, M. N.: A short proof and a generalization of Miranda's existence theorem. Proc. Amer. Math. Soc. 107 (1989), 701-703.
28. WATSON, G. N.: A treatise on the theory of Bessel functions. Cambridge University Press, Cambridge 1966.