Definition of A (S. 183)

n = 20000; b = Table[0, {n}]; 
    b[[1]] = 1;
A = SparseArray[{{i_, i_} -> Prime[i]}, 
                n] + (# + Transpose[#]) &@
          SparseArray[
            Flatten@Table[{i, i + (2^j)} -> 1, {i, n - 1}, {j, 0, 
                  Log[2. , n - i]}], n];

Sitzung S. 195

diagonal = 
      Table[A[[i, i]], {i, n}]; 
    prec = 100; b = SetPrecision[b, prec + 5];
\(\(x = 
        LinearSolve[A, b, 
          Method -> {Krylov, Method -> ConjugateGradient, 
              Preconditioner -> \((#\/diagonal &)\), 
              Tolerance -> 10\^\(\(-prec\) - 1\)}];\)\)
N[x[[1]], 100]