Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems

Abstract

We present a transpose-free version of the nonsymmetric scaled Lanczos procedure. It generates the same tridiagonal matrix as the classical algorithm, using two matrix-vector products per iteration without accessing AT. We apply this algorithm to obtain a transpose-free version of the Quasi-Minimal Residual method of Freund and Nachtigal (without look-ahead), which requires three matrix-vector products per iteration. We also present a related transpose-free version of the Bi-Conjugate Gradients algorithm.