Abstract
In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejér type interpolation in the Lp norm on an arbitrary system of nodes are presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Szabados, J. and Varma, A. K., On Higher Order Hermite-Fejér Interpolation in WeightedL p—Metric, Acta Math. Hungar., 59(1991), 133–140.
Erdës, P., On the Uniform Distribution of the Roots of Certain Polynomials, Ann. of Math., 43(1942), 59–64.
Vértesi, P. and Xu, Y., Truncated Hermite Interpolation Polynomials, Studia Sci. Hungar., 28(1993), 205–213.
Shi, Y. G., Mean Convergence of Lagarange Type Interpolation on an Arbitrary System of Nodes, Acta Math. Appl. Sinica., to appear.
Shi, Y. G., Mean Convergence of Truncated Hermite Interpolation on an Arbitrary System of Nodes, Acta Math. Hungar., 76(1997), 45–58.
Shi, Y. G., On Hermite Interpolation, J. Approx. Theory, 105(2000), 49–86.
Shi, Y. G., Mean Convergence of Interpolatory Processes on Arbitrary System of Nodes, Acta Math. Hungar., 70(1996), 27–38.
Shi, Y. G., Mean Convergence of Hermite Interpolation of High Order on an Arbitrary System of Nodes, Submitted to J. Math. Rearch Expos., to appear.
Shi, Y.G., Truncated Hermite Interpolation on an Arbitrary System of Nodes, J. Approx. Theory., to appear.
Shi, Y. G., Necessary Condition for Mean Convergence of Lagrange Interpolation on an Arbitrary System of Nodes, Acta Math. Hungar., 72(1996), 251–260.
Ditzian, Z. and Totik, V., Moduli of Smoothness, Springer Series in Computational Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1987.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project 19671082 supported by National Natural Science Foundation of China, I acknowledge endless help from Prof. Shi Ying-Guang during finishing this paper.
Rights and permissions
About this article
Cite this article
Yongping, F., Junzhi, C. Mean convergence of Hermite-Fejér type interpolation on an arbitrary system of nodes. Anal. Theory Appl. 20, 199–214 (2004). https://doi.org/10.1007/BF02835289
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02835289