Everywhere divergent extended Hermite - Fejer interpolation process
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Keywords:
Interpolation; Polynomial interpolation; Lagrange interpolation polynomial; Legendre polynomialAbstract
The purpose of this paper is to construct a polynomial of different degree with some conditions in the interval I = [−1,1] by using Hermite - Fejer interpolation polynomial (HFI) of degree at most (4n −1) that agree with f C[1,1] and has zero derivative at each nodes. Also, we investigate all extensions of (HFI) on (−1,1) which are divergent everywhere.
Mathematics Subject Classification (2010):41A05, 41A10
References
Fejér, L., Über Interpolation, Nachrichten der Akademie der Wissenschaften in Göttingen, (1916), 66–91.
Berman, D. L., On the theory of interpolation of a function of a real variable, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 6, (1967), 3–10.
Berman, D. L., On an everywhere divergent process of the Hermite-Fejér interpolation, Izv. Vyss. Ucebn. Zaved Mathematica, 98, (1970), 26–34.
Cook, W. L., Mills, T. M., On Berman’s phenomenon in interpolation theory, Bulletin of the Australian Mathematical Society, 12, (1975), 457–465.
Maky, M., On an extended Hermite–Fejer interpolation process, Journal of al-qadisiyah for pure science (quarterly), 13, (2008), 1–8.
Byrne, G. J., Simon, J. S., On Berman’s phenomenon for (0, 1, 2) Hermite-Fejér interpolation, Journal of Numerical Analysis and Approximation Theory, 48, (2019), 3–15.
Khrajan, M. M., Study of Hermite-Fejer Type Interpolation Polynomial, Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, (2021), 2240–2242.
Berman, D. L., Analysis of convergence of all possible extensions of a Hermite—Fejér interpolation process, Soviet Math. (Iz. VUZ), 28, (1984), 91–93.
Popoviciu, T., Asupra demonstratiei teoremei lui Weierstrass cu ajutorul polinoamelor de interpolare, Lucraarile Sesiunii Generale Stiintifice din, (1950), 2–12.
Berman, D. L., On a property of weirsteras linear poly, Operators, ibid, 21, (1977), 125–126, (in Russian).
Shisha, O., Mond, B., The rapidity of convergence of the Hermite-Fejér approximation to functions of one or several variables, Proc. Amer. Math. Soc., (1966), 1269–1276.
Srivastava, K. B., Oghanna, characterization of all extensions of certain Quasr step-parapolas of higher order, J. of the college of education, Salahaddin university, 3, (1990), 22–39.
Sharma, A., Tzimbalario, J., Quasi-Hermite—Fejér type interpolation of higher order, J. Approx. Theory, 13, (1975), 431–442.
