Artículos de revistas
Zeros Of Classical Orthogonal Polynomials Of A Discrete Variable
Registro en:
Mathematics Of Computation. , v. 82, n. 282, p. 1069 - 1095, 2013.
255718
10.1090/S0025-5718-2012-02646-9
2-s2.0-84873271277
Autor
Area I.
Dimitrov D.K.
Godoy E.
Paschoa V.G.
Institución
Resumen
In this paper we obtain sharp bounds for the zeros of classical orthogonal polynomials of a discrete variable, considered as functions of a parameter, by using a theorem of A. Markov and the so-called Hellmann-Feynman theorem. Comparisons with previous results for zeros of Hahn, Meixner, Kravchuk and Charlier polynomials are also presented. © 2012 American Mathematical Society. 82 282 1069 1095 Andrews, G., Askey, R., Roy, R., Special Functions (1999), Cambridge Univ. Press, CambridgeArea, I., Dimitrov, D.K., Godoy, E., Ronveaux, A., Zeros of Gegenbauer and Hermite polynomials and connection coefficients (2004) Math. Comp., 73, pp. 1937-1951 Area, I., Dimitrov, D.K., Godoy, E., Rafaeli, F.R., Inequalities for zeros of Jacobi polyno- mials via Obrechkoff's theorem (2012) Math. Comp, 81, pp. 991-1004 Björck, A., (1996) Numerical Methods for Least Squares Problems, , SIAM, Philadelphia PA Borodin, A., Ferrari, P.L., Prähofer, M., Sasamoto, T., Fluctuation properties of the TASEP with periodic initial configuration (2007) J. Stat. Phys, 129 (5-6), pp. 1055-1080 Chebyshev, P.L., Interpolation of equidistant nodes, and, on continued fractions (1962) Com- plete Works, USSR Academy of Sciences Publishing House, , Moscow-Leningrad, 1948 French transl., Oeuvres, Chelsea, New York Chihara, T.S., An Introduction to Orthogonal Polynomials (1978), Gordon and Breach, New YorkChihara, L., Stanton, D., Zeros of generalized Krawtchouk polynomials (1990) J. Approx. Theory, 60 (1), pp. 43-57 Dahlquist, G., Björck, A., Numerical Methods (1974), Prentice Hall, Englewood CliffsDimitrov, D.K., On a conjecture concerning monotonicity of zeros of ultraspherical polyno- mials (1996) J. Approx. Theory, 85, pp. 88-97 Dimitrov, D.K., Nikolov, G.P., Sharp bounds for the extreme zeros of classical orthogonal polynomials (2010) J. Approx. Theory, 162, pp. 1793-1804 Dimitrov, D.K., Rafaeli, F.R., Monotonicity of zeros of Jacobi polynomials (2007) J. Approx. Theory, 149, pp. 15-29 Dimitrov, D.K., Rafaeli, F.R., Monotonicity of zeros of Laguerre polynomials (2009) J. Comput. Appl. Math., 233, pp. 699-702 Elbert, Á., Some recent results on the zeros of Bessel functions and orthogonal polynomials (2001) J. Comput. Appl. Math., 133, pp. 65-83 Gelb, A., Platte, R.B., Rosenthal, W.S., The discrete orthogonal polynomial least squares method for approximation and solving partial differential equations (2008) Commun. Comput. Phys., 3, pp. 734-758 Horn, R.A., Johnson, C.R., Matrix Analysis (1985), Cambridge Univ. Press, CambridgeIsmail, M.E., Classical and Quantum Orthogonal Polynomials in One Variable (2005), Cambridge University PressIsmail, M.E., Muldoon, M.E., A discrete approach to monotonicity of zeros of orthogonal polynomials (1991) Trans. Amer. Math. Soc., 323, pp. 65-78 Ismail, M.E., Li, X., Bound on the extreme zeros of orthogonal polynomials (1992) Proc. Amer. Math. Soc, 115, pp. 131-140 Johansson, K., Discrete orthogonal polynomial ensembles and the Plancherel measure (2001) Ann. of Math. (2), 153, pp. 259-296 Karlin, S., McGregor, J., Many server queueing processes with Poisson input and expo- nential service times (1958) Pacific J. Math., 8, pp. 87-118 Jordaan, K., Toókos, F., Interlacing theorems for the zeros of some orthogonal polynomials from different sequences (2009) Appl. Num. Math., 59, pp. 2015-2022 Koekoek, R., Swarttouw, R.F., The Askey-scheme of hypergeometric orthogonal polyno- mials and its q-analogue, Delft University of Technology, Faculty of Technical Mathematics and Informatics (1998) Report no, pp. 17-98. , On-line version Krasikov, I., Bounds for zeros of the Charlier polynomials (2002) Methods Appl. Anal, 9 (4), pp. 599-610 Krasikov, I., On extreme zeros of classical orthogonal polynomials (2006) J. Comput. Appl. Math., 193, pp. 168-182 Krasikov, I., Zarkh, A., On zeros of discrete orthogonal polynomials (2009) J. Approx. Theory, 156, pp. 121-141 Kristinsson, K., Dumonts, G.A., Cross-directional control on paper machines using Gram polynomials (1996) Automatica, 32 (4), pp. 533-548 Kuijlaars, A.B.J., Rakhmanov, E.A., Zero distributions for discrete orthogonal polynomials (1998) J. Comput. Applied Math., 99, pp. 255-274 Markov, A., Sur les racines de certaines équations (second note) (1886) Math. Ann, 27, pp. 177-182 Levit, R.J., The zeros of the Hahn polynomials (1967) SIAM Rev, 9, pp. 191-203 Ronveaux, A., Zarzo, A., Area, I., Godoy, E., Classical orthogonal polynomials: dependence of parameters (2000) J. Comput. Appl. Math, 121, pp. 95-112 Szego, G., Orthogonal Polynomials (1975), 23. , 4th ed. Amer. Math. Soc. Coll. Publ. Providence RIVan Doorn, E.A., Zeifman, A.I., On the speed of convergence to stationarity of the Erlang loss system (2009) Queueing Systems, 63, pp. 241-252