On 11/25, Julius Smith wrote:
>
> I would expect ba.tabulate() to be unbeatable when the function being
> sampled is actually linear, quadratic, or cubic,

Well ;) If the function is cubic then chebtab() will win even with NX=1.
Ignoring the floating point issues, chebtab() will be simply equal to
the approximated function. If the function is "nearly cubic", chebtab()
should likely win anyway, I guess, but this depends.

ba.tabulate() can be better simply because (if we want a fair comparison)
it has more sampling points with the same rdtable size.

For example. chebtab(FX, NX=100,CD=1) creates rdtable of size = 200, so
we should compare it with ba.tabulate(FX,S=200).lin.  And in this case
tabulate().lin will likely win, chebyshev approximation of 1st order is
not much better than linear interpolation if function is smooth enough,
but tabulate().lin has twice more sampling points.

Oleg.



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