Abstract
Properties of Lebesgue function for Lagrange interpolation on equidistant nodes are investigated. It is proved that Lebesgue function can be formulated both in terms of a hypergeometric function,2F1 and Jacobi polynomials. Moreover, an integral expression of Lebesgue function is also obtained and the asymptotic behavior of Lebesgue constant is studied.
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Luttmann, F. W. and Rivlin, T. J., Some Numerical Experiments in the Theory of Polynomial Interpolation, IBM J. Res. Develop., 9(1965), 187–191.
Brutman, L., Lebesgue Functions for Polynomial Interpolation—a Survey, Annals of Numerical Mathematics, 4 (1997), 111–127.
Turetskii, A. H., Theory of Interpolation in Problem Form, Minsk, 1968.
Schönhage, A., Fehlerfortpflanzung bei Interpolation, Numer. Math., 3 (1961), 62–71.
Mills, T. M. and Smith, S. J., The Lebesgue constant for Lagrange interpolation on equidistant nodes, Numer. Math., 61 (1992), 111–115.
Shivakumar, P. N. and Wong, R., Asymptotic Expansion of the Lebesgue Constants Associated with Polynomial Interpolation, Mathematics of Computation, 39 (1982), 195–200.
Brutman, L., Gopengauz I. and Toledano, D., On the Integral of the Lebesgue Function Induced by Interpolation at the Chebyshev Nodes, Acta Math. Hungar., 90 (2001), 11–28.
Fejer, L., Ueber Interpolation, Vorgelegt in der Sitzung, 15(1916), 66–91.
Szegö, G., Orthogonal Polynomials, American Mathematical Society, 1985.
Runge, C., Über Empirische Funktionen und die Interpolation Zwischen äquidistanten Ordinaten, Z. für Math. und Phys., 46 (1901), 224–243.
Knuth, D. E., Graham, R. L. and Patashnik, O., Concrete Mathematics: a Foundation for Computer Science, Addison-Wesley, 1990.
Gradshteyn, I. S. and Ryzhik, I. M., Table of Integrals, Series and Products, Academic Press, 1967.
Gatteschi, L., Funzioni Speciali, UTET, 1973.
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Eisinberg, A., Fedele, G. & Franzè, G. Lebesgue constant for Lagrange interpolation on equidistant nodes. Anal. Theory Appl. 20, 323–331 (2004). https://doi.org/10.1007/BF02835225
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DOI: https://doi.org/10.1007/BF02835225