function?[x?y]?=?newton（Abx0niter）
%[x?y]?=?newton（Abx0niter）;
%solves?the?linear?least?squares?problem?with?nonnegative?variables?using?the?newton‘s?algorithm?in?[1].
%Input:
%???A:??????[MxN]?matrix?
%???b:??????[Mx1]?vector
%???x0:?????[Nx1]?vector?of?initial?values.?x0?>?0.?Default?value:?ones（n1）
%???niter:??Number?of?iterations.?Default?value:?10
%Output
%???x:??????solution
%???y:??????complementary?solution
%
%?[1]?Portugal?Judice?and?Vicente?A?comparison?of?block?pivoting?and
%?interior?point?algorithms?for?linear?least?squares?problems?with
%?nonnegative?variables?Mathematics?of?Computation?63（1994）?pp.?625-643
%
%Uriel?Roque
%02.05.2006

[mn]?=?size（A）;

if?nargin?????x0?=?ones（n1）;
????niter?=?10;
elseif?nargin?????niter?=?10;
end

if?isempty（x0）
????x0?=?ones（n1）;
elseif?any（x0?<=?0）
????disp（‘Error.?The?initial?vector?should?be?nonzero‘）;
????x?=?[];
????y?=?[];
????return
end

AtA?=?A‘*A;
Atb?=?A‘*b;

In?=?e