function sol = NewtonSystemsalpha(F,JF,xzero,tolass,nmax)
% solve a nonlinear system of equations F(x)=0, 
% with differentiable vector function F and 
% Jacobian matrix function JF
c = 10*tolass*ones(size(xzero)); xnext = xzero; iter = 0;
while (norm(c)> tolass || norm(F(xnext))>tolass && iter < nmax)
    xact = xnext;
    c = JF(xact)\(-F(xact));
    Fdir = @(alpha) norm(F(xact + alpha * c));
    alphamin = fminbnd(Fdir,-1,1);
    xnext = xact + alphamin*c;
    iter = iter + 1;
end
sol = xnext;
end