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


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. F.W. Dorr, An example of ill-conditioning in the numerical solution of singular perturbation problems, Math. Comp., 25 (1971), pp. 271-283.

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