Description
The `Dorr' matrix is
A diagonally dominant, tridiagonal,
M-matrix.
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
References
- 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),
pp. 271-283.
The Matrix Market is a service of the
Mathematical and Computational Sciences Division /
Information Technology Laboratory /
National Institute of Standards and Technology
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Page created 1997-03-03, last modified 2000-08-06.
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