Barycentric Lagrange Interpolating Polynomials and Lebesgue Constant

Computes lagrange interpolating polynomials and Lebesgue function/constant.

Description

The first script, barylag.m, performs a barycentric lagrange interpolation on a for a set of given data. This approach follows from a paper by L. N. Trefethen (ref inside script comments), and is much faster than the previous script. Additionally, it has been vectorized to improve computation time even more. The second script, lebesgue.m is for computing the lebesgue function and constant for a set of nodes. If you want to interpolate data using barylag but are using some unusual set of nodes, use the second script to check the lebesgue constant ensure good numerical conditioning.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Lagrange polynomial interpolation

• MATLAB release: MATLAB 6.1 (R12.1)

[Orlando Rodríguez]

An excellent piece of code: very compact, fast and efficient. It is also an excellent example of Matlab's vectorizing capabilities to avoid using "for" loops.