Anyone have any suggestions on books on chebyshev polynomials?

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Discussion Overview

The discussion centers on recommendations for books and resources related to Chebyshev polynomials, particularly their applications in numerical computations. Participants share their experiences and suggest various texts that cover the topic from different perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants find Chebyshev polynomials useful in numerical computations and seek references.
  • One participant mentions using the discrete orthogonality of Chebyshev polynomials to create routines for special functions and integrals, utilizing software like Mathematica or Maxima for high-precision calculations.
  • Several book recommendations are provided, including:
    • Chebyshev and Fourier Spectral Methods by Boyd, noted for its high-level content suitable for graduate courses.
    • Numerical Methods for Scientists and Engineers by Hamming, described as accessible for those with calculus knowledge.
    • Numerical Recipes by Press et al., recognized for its practical sections on Chebyshev polynomials.
  • A participant mentions a recent package developed by Prof. Trefethen for use in Matlab, linking to the relevant publication.
  • Another participant expresses that they are new to Chebyshev polynomials and have downloaded Boyd's book.
  • One participant suggests looking into splines as a related topic.
  • A reference to a book titled "Chebyshev polynomials" by J. C. Mason is also provided.

Areas of Agreement / Disagreement

Participants generally agree on the usefulness of Chebyshev polynomials in numerical computations and share various resources, but there is no consensus on a single best reference or approach.

Contextual Notes

Some discussions may depend on the participants' familiarity with numerical methods and the specific applications they are considering. The recommendations vary in complexity and target audience.

wdlang
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i find that chebyshev polynomials are quite useful in numerical computations

is there any good references?
 
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wdlang said:
i find that chebyshev polynomials are quite useful in numerical computations

is there any good references?

I agree - they are very useful. I have used the discrete orthogonality of them to build nice routines for special functions or integrals I run across (often factor out leading order asymptotic and/or oscillating portions). I usually use something like Mathematica or Maxima to calculate the coefficients to high precision, which I then use in a c or MATLAB routine.

Options I am familiar with include:

Chebyshev and Fourier Spectral Methods, by Boyd (may be free online version). This is pretty high level (for grad course I think) but has tons of stuff in it.

Numerical Methods for Scientists and Engineers, by Hamming. I like this book, and it has a couple of nice chapters on this. Accessible to anyone who knows calculus.

Numerical Recipes, by Press et al., a nice general book that has good, practical sections on chebyshev polynomials. I am familiar with the 2nd edition, which is nice.

Prof. Trefethen has done some nice stuff recently, including leading the development of a nice package that can be used in recent versions of Matlab:
http://www2.maths.ox.ac.uk/chebfun/publications/

good luck!

jason
 
Last edited by a moderator:
jasonRF said:
I agree - they are very useful. I have used the discrete orthogonality of them to build nice routines for special functions or integrals I run across (often factor out leading order asymptotic and/or oscillating portions). I usually use something like Mathematica or Maxima to calculate the coefficients to high precision, which I then use in a c or MATLAB routine.

Options I am familiar with include:

Chebyshev and Fourier Spectral Methods, by Boyd (may be free online version). This is pretty high level (for grad course I think) but has tons of stuff in it.

Numerical Methods for Scientists and Engineers, by Hamming. I like this book, and it has a couple of nice chapters on this. Accessible to anyone who knows calculus.

Numerical Recipes, by Press et al., a nice general book that has good, practical sections on chebyshev polynomials. I am familiar with the 2nd edition, which is nice.

Prof. Trefethen has done some nice stuff recently, including leading the development of a nice package that can be used in recent versions of Matlab:
http://www2.maths.ox.ac.uk/chebfun/publications/

good luck!

jason

thanks a lot

i am new to chebyshev polynomial actually

i have downloaded the book by boyd
 
Last edited by a moderator:
Look at splines, ... then ...
 
you can refer to

Chebyshev polynomials by J. C. Mason
 

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