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Maximal approximation order for a box-spline semi-cardinal interpolation scheme on the three-direction mesh

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Abstract

Let M be the centred 3-direction box-spline whose direction matrix has every multiplicity 2. A new scheme is proposed for interpolation at the vertices of a semi-plane lattice from a subspace of the cardinal box-spline space generated by M. The elements of this ‘semi-cardinal’ box-spline subspace satisfy certain boundary conditions extending the ‘not-a-knot’ end-conditions of univariate cubic spline interpolation. It is proved that the new semi-cardinal interpolation scheme attains the maximal approximation order 4.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Leeds, LS2 9JT, UK

    Aurelian Bejancu

  2. Numerical Geometry Ltd., Lode, Cambridge, CB5 9EP, UK

    Malcolm A. Sabin

Authors
  1. Aurelian Bejancu
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  2. Malcolm A. Sabin
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Corresponding author

Correspondence to Aurelian Bejancu.

Additional information

Communicated by C.A. Micchelli

AMS subject classification

41A15, 41A05, 41A25, 41A63, 39A70, 47B35

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Bejancu, A., Sabin, M.A. Maximal approximation order for a box-spline semi-cardinal interpolation scheme on the three-direction mesh. Adv Comput Math 22, 275–298 (2005). https://doi.org/10.1007/s10444-003-2601-7

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  • DOI: https://doi.org/10.1007/s10444-003-2601-7

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