% generates Table 3.1

n = 4096;
N = 2*n-1; k = 1:N; b = 1 + cumsum(k);
A = 1./(hankel(b(1:n),b(n:N))-ones(n,1)*k(1:n));

vals = [];
for nu = 1:13,
   n=2^(nu-1); An=A(1:n,1:n); vals=[vals;normest(An,5e-12)];
end;

table = vals; result = zeros(size(vals));

for L=10:11
    L2 = 2*L-1; vv = zeros(L2,1); vv(1:2:L2) = vals(1:L);
    for j=2:L
        k=j:2:L2+1-j; vv(k)=vv(k)+1./(vv(k+1)-vv(k-1));
    end;
    result(1:L) = vv(1:2:L2);
    table = [table result];
end

table
