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.
%
%   Copyright (c) 1984-98 by The MathWorks, Inc.
%   $Revision: 1.5 $  $Date: 1997/11/21 23:29:46 $

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