function plotexpnorm(A);
% PLOTEXPNORM  Plots ||expm(tA)|| for given A, on interval 0<t<20.
% Also plots spectral abcissa estimate and the spectrum of A.
% See Tref&Bau 24.4.  ELB 12/03

M=100;
t=linspace(0,20,M+1);
for j=1:M+1
   y(j)=norm(expm(t(j)*A),2);
end
lam=eig(A);
alf=max(real(lam)); % spectral abcissa
subplot(2,1,1)
semilogy(t,y,t,exp(alf*t),'--')
legend('|e^{tA}|_2','e^{t\alpha(A)}')
title('Norm of exponential vs rate predicted from rightmost eigenvalue.')
subplot(2,1,2)
plot(real(lam),imag(lam),'o')
grid on
title('Spectrum (eigenvalues) of A.')