Accurate computation of the zeros of the generalized Bessel polynomials

Numerische Mathematik

Volumn 86, Issue 3, 2000, Pages 507-538

  Pasquini, L ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

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EID: 0034398736     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110000166     Document Type: Article

References (54)

1. Agarwal, R.P. (1954): On the Bessel polynomials. Canadian J. Math. 6: 410-415
2. Al-Salam, W.A. (1957): The Bessel polynomials. Duke Math. J. 24: 529-545
3. Barnes, C.W. (1976): Remarks on the Bessel polynomials. Amer. Math. Monthly 83: 1034-1040
4. Belmehdi, S. (1993): Theorem 8.3. In: W. V. Assche (ed) Open problems, number 48 in J. Comput. Appl. Math., pages 225-243
5. Bochner, S. (1929): Über Sturm-Liouvillesche Polynomsysteme. Math. Zeit. 29: 730-736
6. Bottema, O. (1977): On the zeros of the Bessel polynomials. Nederl. Akad. Wetensh. Proc. Ser. A 80. Also published as Indag. Math. 39: 380-382
7. Bottema, O. (1977): On the zeros of the Bessel polynomials. Nederl. Akad. Wetensh. Proc. Ser. A 80. Also published as Indag. Math. 39: 380-382
8. Brafman, F. (1953): A set of generating functions for Bessel polynomials. Proc. Amer. Math. Soc. 4: 275-277
9. Burchnall, J.L. (1951): The Bessel polynomials. Canadian J. Math. 3: 62-68
10. Carlitz, L. (1957) On the Bessel polynomials. Duke Math. J. 24: 151-162
11. Carpenter, A.J. (1992): Asymptotics for zeros of the generalized Bessel polynomials. Numer. Math. 62: 465-482
12. 1(l;c;x). Nederl. Akad. Wetensch. Proc. Ser. A 79. Also published as Indag. Math. 38: 408-418
13. 1(l;c;x). Nederl. Akad. Wetensch. Proc. Ser. A 79. Also published as Indag. Math. 38: 408-418
14. de Bruin, M.G., Saff, E.B., Varga, R.S. (1981): On the zeros of the generalized Bessel polynomials. I & II. Nederl. Akad. Wetensch. Proc. Ser. A 84(1). Also published as Indag. Math. 43(1): 1-25
15. de Bruin, M.G., Saff, E.B., Varga, R.S. (1981): On the zeros of the generalized Bessel polynomials. I & II. Nederl. Akad. Wetensch. Proc. Ser. A 84(1). Also published as Indag. Math. 43(1): 1-25
16. Dikinson. D. (1954): On Lommel and Bessel polynomials. Proc. Amer. Math. Soc. 5: 946-956
17. Docev, K. (1962): On the generalized Bessel polynomials. Bulgar. Akad. Nauk. Izv. Mat. Inst. 6: 89-94
18. Gautschi, W. (1984): Questions of numerical condition related to polynomials. In: G. H. Golub (ed) Studies in Numerical Analysis, number 24 in Studies in Mathematics, pages 140-177. The Mathematical Association of America
19. Gautschi, W. ( 1991 ): The condition of a problem. A set of lectures given at the University of L'Aquila, Italy
20. Golub, G.H., Robertson, T.N. ( 1967): A generalized Bairstow algorithm. Comm. ACM 10(6): 371-373
21. Golub, G.H., Van Loan, C.F. (1996): Matrix Computations. The Johns Hopkins University Press, Baltimore and London, third edition
22. Golub, G.H., Wilkinson, J.H. ( 1976): Ill-conditioned eigensystems and the computation of the Jordan canonical form. SIAM Review 18: 578-619
23. Greengard, L., Rokhlin, V. (1997): A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numer. 6: 229-269
24. Grosswald, E. (1978): Bessel Polynomials, volume 698 of Lecture Notes in Mathematics. Springer - Verlag, New York
25. Grosswald, E. (1979): Recent applications of some old work of Laguerre. Amer. Math. Monthly 86: 648-658
26. Hrycak, T., Rokhlin, V. (1998): An improved fast multipole algorithm for potential fields. SIAM J. Sci. Comput. 19(6): 1804-1826
27. Ifantis, E.K., Siafarikas, P.D. ( 1988): Bounds for the first positive zero of a mixed Bessel function. J. Comput. Appl. Math. 21: 245-249
28. Ifantis, E.K., Siafarikas, P.D. (1993): On the zeros of a class of polynomials including the generalized Bessel polynomials. J. Comput. Appl. Math. 49: 103-109
29. Ifantis, E.K., Siafarikas, P.D. (1993): Problem 8.1. In: W. V. Assche (ed) Open problems, number 48 in J. Comput. Appl. Math., pages 225-243
30. Kailath, T., Olshevsky, V. (1997): Diagonal pivoting for partially reconstructibie Cauchy-like matrices, with applications to Toeplitz-like linear equations and to boundary rational matrix interpolation problems. Lin. Alg. and Its Applic. 254: 251-302
31. Krall, H.L., Frink, O. (1949): A new class of orthogonal polynomials: the Bessel polynomials. Trans. Amer. Math. Soc. 65: 100-115
32. Lakshmikantham, V., Trigiante, D. (1988): Theory of difference equations: numerical methods and applications. Academic Press. New York
33. Luke, Y.L. (1969): Special Functions and their Approximations, Vol. 2. Academic Press, New York
34. Martinez, J.R. ( 1977): Transfer functions of generalized Bessel polynomials. IEEE CAS 24: 325-328
35. McCarthy, P.J. (1961): Approximate location of the zeros of generalized Bessel polynomials. Quart. J. Math. Oxford Ser. (2) 12: 265-267
36. Olver, F.W.J. (1954): The asymptotic expansions of Bessel functions of large order. Phil. Trans. Roy. Soc. London Ser. A 247: 338-368
37. Parlett, B.N., Reinsch, C. (1969): Balancing a matrix for calculation of eigenvalues and eigenvectors. Numer. Math. 13: 292-304. See also HACLA, pp. 315-326
38. Parlett, B.N., Reinsch, C. (1969): Balancing a matrix for calculation of eigenvalues and eigenvectors. Numer. Math. 13: 292-304. See also HACLA, pp. 315-326
39. Pasquini, L. ( 1989): Polynomial solutions to second order linear homogeneous ordinary differential equations. Properties and approximation. Calcolo 26: 167-183
40. Pasquini, L. (1994): On the computation of the zeros of the Bessel polynomials. In: R. V. M. Zahar (ed) Approximation and Computation, number 119 in International Series of Numerical Mathematics, pages 511-534. Birkhauser Verlag, Basel-Boston-Berlin
41. Pasquini, L., Trigiante, D. (1984): Un nuovo algoritmo ottimizzato per la approssimazione degli zeri di una funzione analitica. Pubbl. dell' I.R.M.A. del CNR, 2
42. Pasquini, L., Trigiante, D. (1985): A globally convergent method for simultaneously finding polynomial roots. Math. Comp. 44: 135-149
43. Pasquini, L., Trigiante, D. (1985): Numerical methods for simultaneously approaching roots of polynomials. In: V. Lakshmikantham (ed) Trends in the theory and practice of non-linear analysis, number 110 in North-Holland Mathematics Studies, pages 363-370. North-Holland, Amsterdam-New York-Oxford
44. Rainville, E.D. ( 1953): Generating functions for Bessel and related polynomials. Canadian J. Math. 5: 104-106
45. Reichel, L., Trefethen, L.N. (1992): Eigenvalues and pseudo-eigenvalues of Toeplitz matrices. Lin. Alg. and Its Applic., 162-164: 153-185
46. Romanovsky, V. (1929): Sur quelques classes nouvelles des polynômes orthogonaux. C. R. Acad. Sci. Paris 188: 1023-1025
47. Saff, E.B., Varga, R.S. (1976): On the sharpness of theorems concerning zero-free regions for certain sequences of polynomials. Numer. Math. 26: 345-354
48. Saff, E.B., Varga, R.S. (1976): Zero-free parabolic regions for sequences of polynomials. SIAM J. Math. Anal. 7: 344-357
49. z. III. Numer. Math. 30: 241-266
50. Toscano, L. (1955): Osservazioni, confronti e complementi su particolari polinomi ipergeometrici. Le Matematiche 10: 121-133
51. Trefethen, L.N. (1992): Pseudospectra of matrices. In: D. F. Griffiths, G. Watson (eds) Numerical Analysis 1991, number 260, pages 234-266. Longman
52. UnderHill, C. (1972): On the zeros of generalized Bessel polynomials. Technical report, University of Salford
53. Wimp, J. (1965): On the zeros of a confluent hypergeometric function. Proc. Amer. Math. Soc. 16: 281-283
54. Wragg, A., Underhill, C. ( 1976): Remarks on the zeros of the Bessel polynomials. Amer. Math. Monthly 83: 122-126