function [Hv] = H0vec(v, usr_par)
% 
% compute H0*v, where H0 is the initial BFGS matrix
% H0 is a replacement of the inverse of the Hessian of f!
%
% Version June 6, 2008
% Matthias Heinkenschloss
%

% We use global variables to pass information to the
% functions that compute the solution of Burgers equation, etc.

global BURGERS_GLB


omega  = BURGERS_GLB.omega;
Hv     = zeros(size(v));

% use omega*I  as initial Hessian approx.
%Hv = v/omega;
%return;
    
% use omega*dt*Q  as initial Hessian approx.
Deltat = BURGERS_GLB.Deltat;   % length of time interval
dt2    = Deltat/2;
nt     = BURGERS_GLB.nt;       % number of time intervals
nx     = BURGERS_GLB.nx;       % number of spatial intervals
nu     = nx+1;                 % number of u-variables per time step

Hv(1:nu) = (omega*dt2)\(BURGERS_GLB.Q\v(1:nu));
for i = 2:nt
        Hv((i-1)*nu+1:i*nu) = (omega*Deltat)\(BURGERS_GLB.Q\v((i-1)*nu+1:i*nu));
end
i = nt+1;
Hv((i-1)*nu+1:i*nu) = (omega*dt2)\(BURGERS_GLB.Q\v((i-1)*nu+1:i*nu));