The `Dorr' matrix is
A diagonally dominant, tridiagonal,
It is ill conditioned
for small values of the (positive) parameter, theta.
The columns of the inverse of this matrix vary greatly in norm.
The first and last elements are row-diagonally dominant where
The amount of diagonal dominance is given by (ignoring rounding errors):
|A1,1|-|A1,2| = THETA*(N+1)^2
|AN,N|-|AN,N-1| = THETA*(N+1)^2
- This generator is adapted from Nicholas J. Higham's
Test Matrix Toolbox.
- F.W. Dorr, An example of ill-conditioning in the numerical
solution of singular perturbation problems, Math. Comp., 25 (1971),
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Page created 1997-03-03, last modified 2000-08-06.