0

Next, let's discuss the discrete setup. Since we seek an *even*
extension of the upper semi-circle we consider the case of *even*
number of grid points - equally distributed along the unit circle.
There are two main choices: one
choice is to consider only the *interior* points,
(here,
and ).
This yields
the so called
Gauss-Chebyshev points, consult §2.5.1 below,

The second choice takes into
account also the -boundaries, considering
(here, and
*r*=0),
which yield the so called Gauss-Lobatto-Chebyshev points - consult
§2.5.2 below,

- Chebyshev interpolant at Gauss gridpoints
- Chebyshev interpolant at Gauss-Lobatto gridpoints
- Exponential convergence of Chebyshev expansions
- Chebyshev differentiation matrix

Thu Jan 22 19:07:34 PST 1998