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Convergence of Local Variational Spline Interpolation
Journal of Mathematical Analysis and Applications
  • Scott N. Kersey, Georgia Southern University
  • Ming-Jun Lai, University of Georgia
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In this paper we first revisit a classical problem of computing variational splines. We propose to compute local variational splines in the sense that they are interpolatory splines which minimize the energy norm over a subinterval. We shall show that the error between local and global variational spline interpolants decays exponentially over a fixed subinterval as the support of the local variational spline increases. By piecing together these locally defined splines, one can obtain a very good C0 approximation of the global variational spline. Finally we generalize this idea to approximate global tensor product B-spline interpolatory surfaces.

Citation Information
Scott N. Kersey and Ming-Jun Lai. "Convergence of Local Variational Spline Interpolation" Journal of Mathematical Analysis and Applications Vol. 341 Iss. 1 (2008) p. 398 - 414 ISSN: 0022-247X
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