Quasi-Interpolation on Irregular Points

  • E. W. Cheney
  • Junjiang Lei
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)

Abstract

A quasi-interpolant is an operator L having the form
$$Lf = \sum\limits_{i = 1}^\infty {f\left( {{y_i}} \right){g_i}} .$$
(1.1)
The points y i are called “nodes”; they are prescribed in ℝ n . The entities g i are prescribed functions from ℝ n to ℝ. The case of irregularly situated nodes is of particular interest. We investigate the question of how to select the “base functions” g i in order to obtain favorable estimates of ∥Lf - f∥.

Keywords

Radial Basis Function General Position Lagrange Interpolation Lagrange Polynomial Vandermonde Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • E. W. Cheney
    • 1
  • Junjiang Lei
    • 1
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA

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