A fast realization of preconditioned Conjugate Gradients for Wiener-Hopf integral equations

We present an efficient implementation of the Conjugate Gradients algorithm for Wiener-Hopf integral equations based on finite rank approximations of the integral operator and the corresponding preconditioner. The resulting algorithm is of linear complexity. Numerical experiments with this implementation of the preconditioned Conjugate Gradients algorithm show significant speed-up in the ill-conditioned case. This algorithm acts on ill-conditioned equations as a regularization algorithm.