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# On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling

@article{Freund1994OnTU, title={On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling}, author={Roland W. Freund and Marlis Hochbruck}, journal={Numerical Lin. Alg. with Applic.}, year={1994}, volume={1}, pages={403-420} }

- Published 1994 in Numerical Lin. Alg. with Applic.
DOI:10.1002/nla.1680010406

Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix-vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving… CONTINUE READING

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