%! Solves the quadratic matrix equation AX^2 + BX + C = 0 with a Newton algorithm.
%! @sp 2
%! @strong{Inputs}
%! @sp 1
%! @table @ @var
%! @item A
%! Square matrix of doubles, n*n.
%! @item B
%! Square matrix of doubles, n*n.
%! @item C
%! Square matrix of doubles, n*n.
%! @item tol
%! Scalar double, tolerance parameter.
%! @item maxit
%! Scalar integer, maximum number of iterations.
%! @item line_search_flag
%! Scalar integer, if nonzero an exact line search algorithm is used.
%! @item X
%! Square matrix of doubles, n*n, initial condition.
%! @end table
%! @sp 1
%! @strong{Outputs}
%! @sp 1
%! @table @ @var
%! @item X
%! Square matrix of doubles, n*n, solution of the matrix equation.
%! @item info
%! Scalar integer, if nonzero the algorithm failed in finding the solution of the matrix equation.
%! @end table
%! @sp 2
%! @strong{This function is called by:}
%! @sp 2
%! @strong{This function calls:}
%! @sp 1
%! @ref{fastgensylv}
%! @sp 2
%! @strong{References:}
%! @sp 1
%! N.J. Higham and H.-M. Kim (2001), "Solving a quadratic matrix equation by Newton's method with exact line searches.", in SIAM J. Matrix Anal. Appl., Vol. 23, No. 3, pp. 303-316.
%! @sp 2
%! @end deftypefn
%@eod:
% Copyright (C) 2012 Dynare Team
%
% This file is part of Dynare.
%
% Dynare is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% Dynare is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with Dynare. If not, see <http://www.gnu.org/licenses/>.