Minimizing storage in implementations of the overlap lattice-Dirac operator

The overlap lattice-Dirac operator contains the sign function $ϵ(H)$. Recent practical implementations replace $ϵ(H)$ by a ratio of polynomials, $H{P}_n(H^2)\mathrm{/}{Q}_n(H^2)$, and require storage of $2n+2$ large vectors. Here I show that one can use only 4 large vectors at the cost of executing the core conjugate algorithm twice. The slow-down might be less than by a factor of 2, depending on the architecture of the computer one uses.