Hans Johnston May 14 2004
I wrote a program to compute D2, extract the interior, and then find the
evals and evectors. The results match, at least to roundoff, MATLAB
results. Note that MATLAB produces the eigenvalues in EXACTLY the same
order since they use LAPACK.
I compute D1 and D2 using a different algorithm then that given in
Trefethen's cheb.m. I'll explain the reason for the change later.
Note also that I index from 0:m, thus D2int(1:m-1,1:m-1), and that my
CHEBD program only asks for m. I suggest starting indices from 0 for
problems with boundaries.
I will work on (hopefully) in the next few days a Poisson solver. I have
never used FFTW, although will do so in the future. In the meantime I
will use the vfftpk.f routines since I am very familiar with them. Using
the REAL transform is very straightforward.