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.
- Bi-conjugate gradients algorithm
- Krylov subspace methods
- Lanczos algorithm
- Nonsymmetric linear systems
- Quasi-minimal residual algorithm
ASJC Scopus subject areas
- Applied Mathematics