Transpose-Free Quasi-Minimal Residual Methods for Non-Hermitian Linear Systems

Recently, Freund and Nachtigal proposed a novel conjugate gradient-type method, the quasi-minimal residual algorithm (QMR), for the iterative solution of general non-Hermitian systems of linear equations. The QMR method is based on the nonsymmetric Lanczos process, and thus, like the latter, QMR requires matrix-vector multiplications with both the coefficient matrix of the linear system and its transpose. However, in certain applications, the transpose is not readily available, and generally, it is desirable to trade in multiplications with the transpose for matrix-vector products with the original matrix.

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