Numerical Analysis: Weierstrass & Fourier Analysis

[talisman2212]

Hi, I am reading numerical analysis and I am very interested in Weierstrass Theorem and Fourier analysis. I want to know what are the similarities and the differences using polynomial approximation and Fourier aproximation for a function and which approximation converge faster and better to a function?
I need much help on this, I can't find yet anything.

 

[mathman]

There is no simple answer. It depends very much on the application of interest.

 

[talisman2212]

The application of interest is on approximation of functions of one variable.

 

[mathman]

Are you concerned with finite or infinite domain? Are the functions continuous? What is the metric used to define the approximation? There may be other questions as well.

 

[talisman2212]

with finite domain, continuous functions and the Euclidean metric.

 

[mathman]

I'll assume you mean d(f,g) = max|f(x)-g(x)| over domain. In this case, a polynomial approximation may be better. The following may be useful.

http://en.wikipedia.org/wiki/Approximation_theory