b=rand(2*N2,1);
rho=norm(b);
[Q,T]=Lanczos((A3-eye(512))'*(A3-eye(512)),b,200);
[N,k]=size(Q);
e1=zeros(k-1,1); e1(1)=1;
y=sqrtm(T)\e1*rho;
x=(A3-eye(512))*Q(:,1:k-1)*y;
[U_W,S_W,V_W]=svd(A3-eye(512));
V=U_W*V_W';
z=V*b;
norm(z-x)
D=eye(512)+V;
eigD=eig(D);
plot(eigD,'+')
m=0.0001;
D=(1+m)/2*eye(512)+(1-m)/2*V;
b=zeros(512,1);b(1)=1;
[x,rr] = CGNE(D,b,zeros(512,1),1e-12,200);
semilogy(1:2:2*max(size(rr)),rr,'-;CGNE;')
hold
[x,rr] = SCG(D,b,zeros(512,1),1e-12,200);
semilogy(rr,'-.;SCG;')
[rr,x] = SUMR(b,V,(1+m)/2,(1-m)/2,1e-12,200);
semilogy(rr,':;SUMR;')
xlabel("# matrix-vector")
ylabel("residual norm")
replot
gset terminal postscript
gset out "gw_conv_hist.ps"
replot
gset terminal x11
hold