Anyone have any suggestions on books on chebyshev polynomials?

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
 
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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
 
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Look at splines, ... then ...
 
you can refer to

Chebyshev polynomials by J. C. Mason
 
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