research-article

Best Constrained Approximation in Hilbert Space and Interpolation by Cubic Splines Subject to Obstacles

Authors:

Lars-Erik Andersson,

Tommy ElfvingAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 16, Issue 5

Pages 1209 - 1232

https://doi.org/10.1137/0916070

Published: 01 September 1995 Publication History

Abstract

We review a Lagrangian parameter approach to problems of best constrained approximation in Hilbert space. The variable is confined to a closed convex subset of the Hilbert space and is also assumed to satisfy linear equalities. The technique is applied to the problem of interpolation of data in a plane by a cubic spline function which is subject to obstacles. The obstacles may be piecewise cubic polynomials over the original knot set. A characterization result is obtained which is used to develop a Newton-type algorithm for the numerical solution.

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Cited By

Luo ZPeng X(2006)A C1-rational spline in range restricted interpolation of scattered dataJournal of Computational and Applied Mathematics10.1016/j.cam.2005.07.010194:2(255-266)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1016/j.cam.2005.07.010
Fredenhagen SOberle HOpfer G(1999)On the Construction of Optimal Monotone Cubic Spline InterpolationsJournal of Approximation Theory10.1006/jath.1998.324796:2(182-201)Online publication date: 1-Feb-1999
https://dl.acm.org/doi/10.1006/jath.1998.3247

Index Terms

Best Constrained Approximation in Hilbert Space and Interpolation by Cubic Splines Subject to Obstacles
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
    2. Numerical analysis
      1. Computations on polynomials
      2. Interpolation
  2. Probability and statistics
    1. Probabilistic representations
2. Theory of computation
  1. Design and analysis of algorithms

Index terms have been assigned to the content through auto-classification.

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cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 16, Issue 5

Sep 1995

221 pages

ISSN:1064-8275

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Copyright © 1995 Society for Industrial and Applied Mathematics.

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 September 1995

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Cited By

Luo ZPeng X(2006)A C1-rational spline in range restricted interpolation of scattered dataJournal of Computational and Applied Mathematics10.1016/j.cam.2005.07.010194:2(255-266)Online publication date: 1-Oct-2006
https://dl.acm.org/doi/10.1016/j.cam.2005.07.010
Fredenhagen SOberle HOpfer G(1999)On the Construction of Optimal Monotone Cubic Spline InterpolationsJournal of Approximation Theory10.1006/jath.1998.324796:2(182-201)Online publication date: 1-Feb-1999
https://dl.acm.org/doi/10.1006/jath.1998.3247

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