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Yorick Master

Joined: Mon Nov 22, 2004 9:43 am
Posts: 354
Location: Livermore, CA, USA
Post rcheby.i
There is a new package, rcheby.i, in the distribution i/ directory, which offers a slightly different take on both rational and polynomial Chebyshev fits than what is available in cheby.i. I also added a routine in cheby.i (cheby_conv) to make it easy to convert back and forth between ordinary polynomial coefficients and Chebyshev coefficients. The rcheby and cheby packages are designed to interoperate.

The difference between rcheby and cheby has to do with the nature of the fits: The cheby package uses a very simple procedure to based on the discrete orthogonality of Chebyshev polynomials to find a polynomial fit that is roughly analogous to a truncated Taylor series. The rcheby package takes the "minimum maximum deviation" property of the Chebyshev polynomials much more seriously, and delivers a fit with the coefficients tweaked to be closer to a true minimax error fit. It also extends the fitting to rational functions as well as polynomials.

The rcheby.i functions were inspired by Dave Bailey's transcription of the function ratlsq given in section 5.13 of Numerical Recipes.

Sun May 30, 2010 10:48 am
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