function G = grcar(n, k)
%GRCAR     Grcar matrix - a Toeplitz matrix with sensitive eigenvalues.
%          GRCAR(N, K) is an N-by-N matrix with -1s on the
%          subdiagonal, 1s on the diagonal, and K superdiagonals of 1s.
%          The default is K = 3.  The eigenvalues of this matrix form an
%          interesting pattern in the complex plane (try PS(GRCAR(32))).

%          References:
%          J.F. Grcar, Operator coefficient methods for linear equations,
%               Report SAND89-8691, Sandia National Laboratories, Albuquerque,
%               New Mexico, 1989 (Appendix 2).
%          N.M. Nachtigal, L. Reichel and L.N. Trefethen, A hybrid GMRES
%               algorithm for nonsymmetric linear systems, SIAM J. Matrix Anal.
%               Appl., 13 (1992), pp. 796-825.

if nargin == 1, k = 3; end

G = tril(triu(ones(n)), k) - diag(ones(n-1,1), -1);