Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems (Q1127054)

A transpose-free version of the nonsymmetric scaled Lanczos procedure is presented. It generates the same tridiagonal matrix as the classical algorithm, using two matrix-vector products per iteration without accessing the transpose of the matrix. This algorithm is applied to obtain a transpose-free version of the quasi-minimal residual method (without look-ahead), which requires three matrix-vector products per iteration. A related transpose-free version of the bi-conjugate gradient algorithm is also presented.