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Z-splines: Moment conserving cardinal spline interpolation of compact support for arbitrarily spaced data

by J. T. Becerra Sagredo

(Report number 2003-10)

Abstract
The Z-splines are moment conserving cardinal splines of compact support. They are constructed using Hermite-Birkhoff curves that reproduce explicit finite difference operators computed by Taylor series expansions. These curves are unique. The Z-splines are explicit piecewise polynomial interpolation kernels of cumulative regularity and accuracy. They are succesive spline approximations to the perfect reconstruction filter {\it sinc(x)}. It is found that their interpolation properties: quality, regularity, approximation order and discrete moment conservation, are related to a single basic concept: the exact representation of polynomials by a long enough Taylor series expansion.

Keywords: interpolation, splines, approximation, moment, conservation, piecewise polynomials, Vandermonde matrix, finite differences, Hermite interpolation

@Techreport{B03_322,
  author = {J. T. Becerra Sagredo},
  title = {Z-splines: Moment conserving cardinal spline interpolation of compact support for arbitrarily spaced data},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2003-10},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2003/2003-10.pdf },
  year = {2003}
}

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