|
|
Spectral Methods
| Speaker: |
Charles Chilaka
|
| Date: |
Wednesday October 17, 2007 |
| Title: |
Polynomial
Approximation: The Fourier System
|
|
Abstract
|
The expansion of a function in terms
of an infinite sequence of orthogonal functions is important in many
numerical methods of approximation. One of the most familiar results
are those for periodic functions expanded in Fourier series. This
expansion introduces a linear transformation between the function and
the sequence of its expansion coefficients and by completeness of the
inner product space; we can still invert this transformation.
We will try to use this idea to see what can be done in the Fourier
system, the problems that may be encountered and how to get over them.
|
|
