The `Kahan' matrix is an upper trapezoidal matrix that has some interesting properties regarding estimation of condition and rank.

To ensure that the QR factorization with column pivoting does not interchange columns in the presence of rounding errors, the diagonal elements are perturbed by PERTURBATION*EPSILON*(N+1-i), where EPSILON is the double precision epsilon. The default value of the perturbation (25) ensures no interchanges up to at least N = 90 in IEEE arithmetic, for the default value of Theta (1.2). For square matrices, the inverse is known explicitly and can be computed here.


  1. This generator is adapted from Nicholas J. Higham's Test Matrix Toolbox.
  2. The diagonal perturbation was suggested by Christian Bischof.
  3. W. Kahan, Numerical linear algebra, Canadian Math. Bulletin, 9 (1966), pp. 757-801.
  4. N.J. Higham, A survey of condition number estimation for triangular matrices, SIAM Review, 29 (1987), pp. 575-596.

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Page created 1997-03-03, last modified 2000-08-06. [ ]