Alternative to domain wall fermions

We define a sparse Hermitian lattice Dirac matrix H coupling $2n+1$ Dirac fermions. When $2n$ fermions are integrated out the induced action for the last fermion is a rational approximation to the Hermitian overlap Dirac operator. We provide rigorous bounds on the condition number of H and compare them to bounds for the higher dimensional Dirac operator of domain wall fermions. Our main conclusion is that overlap fermions should be taken seriously as a practical alternative to domain wall fermions in the context of numerical QCD.