function T = lesp(n)
%LESP Tridiagonal matrix with real, sensitive eigenvalues.
%   GALLERY('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:
%   [1] 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.
%   [2] L. N. Trefethen, Pseudospectra of matrices,
%       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.
%
%   Nicholas J. Higham, Dec 1999.
%   Copyright 1984-2002 The MathWorks, Inc. 
%   $Revision: 1.10 $  $Date: 2002/04/15 03:42:53 $

x = 2:n;
T = full(tridiag( ones(size(x))./x, -(2*[x n+1]+1), x));