--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/grcar.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,18 @@
+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);