Anyone have any suggestions on books on chebyshev polynomials?

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SUMMARY

Chebyshev polynomials are essential in numerical computations, particularly for their discrete orthogonality properties. Key references include "Chebyshev and Fourier Spectral Methods" by Boyd, "Numerical Methods for Scientists and Engineers" by Hamming, and "Numerical Recipes" by Press et al. Tools such as Mathematica and Maxima are commonly used for high-precision coefficient calculations, which can then be implemented in C or MATLAB routines. Additionally, the Chebfun package developed by Prof. Trefethen enhances MATLAB's capabilities for working with Chebyshev polynomials.

PREREQUISITES
  • Understanding of Chebyshev polynomials and their applications in numerical analysis
  • Familiarity with numerical methods and their implementation
  • Proficiency in programming with C or MATLAB
  • Basic knowledge of calculus for comprehending referenced texts
NEXT STEPS
  • Explore "Chebyshev and Fourier Spectral Methods" by Boyd for advanced techniques
  • Study "Numerical Methods for Scientists and Engineers" by Hamming for practical applications
  • Learn about the Chebfun package for MATLAB to enhance computational efficiency
  • Investigate the implementation of Chebyshev polynomials in C programming
USEFUL FOR

Mathematicians, engineers, and computer scientists interested in numerical analysis, particularly those working with polynomial approximations and numerical methods.

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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