On trigonometric and paratrigonometric Hermite interpolation

Authors:
Jinyuan Du;Huili Han;Guoxiang Jin
Affiliations:
Department of Mathematics, Wuhan University, Wuhan, 430072, PR China and Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, PR China;Department of Mathematics, Wuhan University, Wuhan, 430072, PR China and School of Mathematics and Computer, Ningxia University, Yinchuan 750021, Ningxia, PR China;School of Computer Science, Wuhan Institute of Chemical Technology, Wuhan 430073, PR China
Venue:
Journal of Approximation Theory
Year:
2004

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Abstract

In this paper, both trigonometric and paratrigonometric Hermite interpolation for any number of interpolation points with different multiplicities are constructed. The convergence of the Hermite trigonometric interpolation operator for 2π-periodic function and the Hermite paratrigonometric interpolation operator for 2π-antiperiodic function are given when the interpolated functions possess certain analyticity.