User Guide 027

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16 Appendix F: Piecewise Lagrangian Polynomial Interpolation

Piecewise polynomials in Lagrange form are given by

  (16-1)

where

yj= interpolation data values corresponding to xj
n = order or the interpolation polynomial
lj(x) = Lagrange basis polynomials given by
  (16-2)

The Lagrange basis polynomials are such that

  ( 16-3)

One advantage of using Lagrange polynomials is that the interpolation weights (Lagrange basis functions lj ) are not a function of yj . This prop-erty is useful when many interpolations are needed for the same xj but different yj such as in the case of interpolating spatial datasets in time.