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The Non-Periodic Problem -- The Chebyshev Interpolant


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,

Eitan Tadmor
Thu Jan 22 19:07:34 PST 1998