Page 152 - Compact Numerical Methods For Computers

The generalised symmetric matrix eigenvalue problem 141

Gauss elimination run on a Data General NOVA in 23-bit binary arithmetic.
The particular basis functions (11.25) are, as it turns out, rather a poor set to
choose since no matter what exponential parameter a is chosen, the matrix B as
given by (11.29) suffers large differences in scale in its elements. To preserve the
symmetry of the problem, a diagonal scaling could be applied, but a better idea is
to use basic functions which are already orthogonal under the inner product
defined by (11.29). These are the Hermite functions (Newing and Cunningham
1967). As the details of the solution are not germane to the discussion, they will
not be given.
BASIC program code to compute the matrix elements for this problem has been given
in Nash (1984a, §18-4, in particular the code on p 242). The reader is warned that
there are numerous misprints in the referenced work, which was published about the
time of the failure of its publisher. However, the BASIC code, reproduced photogra-
phically, is believed to be correct.