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. Author manuscript; available in PMC: 2014 Nov 15.
Published in final edited form as: Comput Theor Chem. 2013 Nov 15;1024:34–44. doi: 10.1016/j.comptc.2013.09.021

  1. Let l = 0. Compute residue r0 = b − Ax0 and set ν1 = r0/||r0||.

  2. Let l = l + 1.

  3. Use the Arnoldi iteration to construct vector νl+1 that is orthogonal to νk, k = 0, …, l.

  4. Minimize the residue along the new vector νl+1 and update xl.

  5. Calculate the norm of residues ||rl||. If ||rl||/||b|| is less than a predefined convergence threshold δ, output xl as the solution. Otherwise go to step 2.