Anyone have any suggestions on books on chebyshev polynomials?

[wdlang]

i find that chebyshev polynomials are quite useful in numerical computations

is there any good references?

 

[jasonRF]

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

 

[wdlang]

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

 

[michaelc187]

Look at splines, ... then ...

 

[alomari2010]

you can refer to

Chebyshev polynomials by J. C. Mason