Abstract
The purpose of this note is to present bases of the exponential eigen spline spaces in the space of bivariate spline functions of degree d and smoothness p on the type-2 triangulation. The order of smoothness p may be arbitrary, but the degree d is supposed to be the minimal degree for which there exist compactly supported spline functions, when the smoothness is given. It turns out that the exponential eigen sphnes corresponding to the eigenvalues pair (z1,z2) ∈ C 2 can be expressed by means of translates of (quasi) minimal supported spline functions in case 1 ∉ {z1,z2,z2,z2,z1/z2}. If at least one of these numbers is equal to 1, then the exponential eigen splines reduce to in fact univariate exponential eigen sphnes or eigen splines for the type-1 triangulation.
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ter Morsche, H. (1990). On the Exponential Eigen Splines: Type-2 Triangulation. In: Haußmann, W., Jetter, K. (eds) Multivariate Approximation and Interpolation. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 94. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5685-0_16
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DOI: https://doi.org/10.1007/978-3-0348-5685-0_16
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