function delta = findDeltaLM(H)
%FINDDELTA  use Gerschgorin theorem in Levenberg-Marquardt.
%  delta = findDeltaLM(H) tries to find the parameter delta in 
%  Levenberg-Marquardt method:for hessian H,use Gerschgorin 
%  theorm to find the lower bound of eigenvalues, then shift 
%  the bound above the desired (e.g.,.01 * norm(H,inf)).
%
%   See also MODIFIEDCHOL.

% Dianne P. O'Leary oleary@cs.umd.edu 
% Geping Liu geping@math.umd.edu
% 09-21-06

centers = diag(H);
radii = sum(abs(H),2) - abs(centers);

eigLowerBound = min(centers - radii);
desiredBound = 10^(-2) * norm(H,inf);

if eigLowerBound >= desiredBound,
    delta = 0;
    return;
else
    delta = desiredBound - eigLowerBound;
    return;
end