function [u2d,stats]=altsw(m,rhs2d,uin,overlap)
% ALTSW Alternating Schwarz solver
%
% function [u2d,stats]=altsw(m,rhs2d,uin,overlap)
%
maxit=10;
stats=zeros(maxit,1);
m2=overlap-1+((m+1)/2); h=1/(m+1);
al=pmat2(m,m2,h);
u2d=uin;
%
% lower block
%
mr=m2; 
for i=1:maxit
    uold=u2d;
    blow=u2d(1:m,mr+1)*h^-2;
    rlow=rhs2d(1:m,1:mr);
    rlow(1:m,m2)=rlow(1:m,mr)+blow;
    rl=rlow(:);
    ul=al\rl;
    v=zeros(m,m2); v(:)=ul;
    u2d(1:m,1:mr)=v;
%
% upper block
%
    ml=.5*(m+1)+1-overlap;
    bup=u2d(1:m,ml-1)*h^-2;
    rup=rhs2d(1:m,ml:m);
    rup(1:m,1)=rup(1:m,1)+bup;
    rr=rup(:);
    ur=al\rr;
    v=zeros(m,m2); v(:)=ur;
    u2d(1:m,ml:m)=v;
    stats(i)= max(max(u2d-uold));
end