--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/lesp.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,22 @@
+function T = lesp(n)
+%LESP   A tridiagonal matrix with real, sensitive eigenvalues.
+%       LESP(N) is an N-by-N matrix whose eigenvalues are real and smoothly
+%       distributed in the interval approximately [-2*N-3.5, -4.5].
+%       The sensitivities of the eigenvalues increase exponentially as
+%       the eigenvalues grow more negative.
+%       The matrix is similar to the symmetric tridiagonal matrix with
+%       the same diagonal entries and with off-diagonal entries 1,
+%       via a similarity transformation with D = diag(1!,2!,...,N!).
+
+%       References:
+%       H.W.J. Lenferink and M.N. Spijker, On the use of stability regions in
+%            the numerical analysis of initial value problems,
+%            Math. Comp., 57 (1991), pp. 221-237.
+%       L.N. Trefethen, Pseudospectra of matrices, in Numerical Analysis 1991,
+%            Proceedings of the 14th Dundee Conference,
+%            D.F. Griffiths and G.A. Watson, eds, Pitman Research Notes in
+%            Mathematics, volume 260, Longman Scientific and Technical, Essex,
+%            UK, 1992, pp. 234-266.
+
+x = 2:n;
+T = full(tridiag( ones(size(x))./x, -(2*[x n+1]+1), x));