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));