Abstract
We describe three methods for the construction of the fundamental splines of periodic Hermite interpolation in the case of equidistant lattices. Apart from the generalized Euler-Frobenius polynomials our main tools are the discrete Fourier transform, a complex line integral representation and a certain eigenvalue problem for the computation of null splines.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lee, D. (1986) A simple approach to cardinal Lagrange and periodic Lagrange splines. J. Approximation Theory 47, 93–100
Lee, S.L. and A. Sharma (1976) Cardinal lacunary interpolation by g-splines I. The characteristic polynomials. J. Approximation Theory 16, 85–96
Lipow, P.R. and I.J. Schoenberg (1973) Cardinal interpolation and spline functions III. Cardinal Hermite interpolation. Linear Algebra and Its Appl. 6, 273–304
Meinardus, G. und G. Merz (1980) Hermite-Interpolation mit periodischen Spline-Funktionen. Numerical Methods of Approximation Theory, ISNM 52 (Birkhäuser, Basel), 200-210
Merz, G. und W. Sippel (to appear) Zur Konstruktion periodischer Hermite-Interpolationssplines bei äquidistanter Knotenverteilung. J. Approximation Theory
Reimer, M. (1982) Extremal spline bases. J. Approximation Theory 36, 91–98
Reimer, M. and D. Siepmann (1986) An elementary algebraic representation of polynomial spline interpolants for equidistant lattices and its condition. Numer. Math. 49, 55–65
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer Basel AG
About this chapter
Cite this chapter
Merz, G. (1987). The Fundamental Splines of Periodic Hermite Interpolation for Equidistant Lattices. In: Collatz, L., Meinardus, G., Nürnberger, G. (eds) Numerical Methods of Approximation Theory/Numerische Methoden der Approximationstheorie. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 81. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6656-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6656-9_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6657-6
Online ISBN: 978-3-0348-6656-9
eBook Packages: Springer Book Archive