%%%%%%    Nonlinear Equations with Jacobian      %%%%%%%%%%%%%%%%%%%%%%%%%
% Solve routine for the system of equations below. Consider the problem of 
% finding a solution to a system of nonlinear equations whose Jacobian is 
% sparse. The dimension of the problem in this example is 1000. The goal is
% to find x such that F(x) = 0. The nonlinear equations are as follows:
%   F(1)=3(x_1)-2(x_1)^2-2(x_2)+1
%   F(i)=3(x_i)-2(x_i)^2-2(x_i-1)-2(x_i+1)+1
%   F(n)=3(x_n)-2(x_n)^2-(x_n-1)+1
%  with n = 1000.
% To solve a large nonlinear system of equations, F(x)=0, use the 
% large-scale method available in fsolve.
% 
% See function [F,J] = nleqwj(x);

xstart=-ones(1000,1);
fun=@nleqwj; 
options=optimset('Display','iter','LargeScale','on','Jacobian','on');
[x,fval,exitflag,output] = fsolve(fun,xstart,options);

% The MathWorks, Matlab7. Copyright (c).