# A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems

@article{Chan1994AQR, title={A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems}, author={Tony F. Chan and Efstratios Gallopoulos and Valeria Simoncini and Tedd Szeto and Charles H. Tong}, journal={SIAM J. Sci. Comput.}, year={1994}, volume={15}, pages={338-347} }

Motivated by a recent method of Freund [SIAM J. Sci. Comput., 14 (1993), pp. 470–482], who introduced a quasi-minimal residual (QMR) version of the conjugate gradients squared (CGS) algorithm, a QMR variant of the biconjugate gradient stabilized (Bi-CGSTAB) algorithm of van der Vorst that is called QMRCGSTAB, is proposed for solving nonsymmetric linear systems. The motivation for both QMR variants is to obtain smoother convergence behavior of the underlying method. The authors illustrate this…

## 118 Citations

### A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems

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A 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed for the iterative solution of large sparse nonsymmetric linear systems.

### A 1-norm quasi-minimal residual variant of the Bi-CGSTAB algorithm for nonsymmetric linear systems

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A 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed for the iterative solution of large sparse nonsymmetric linear systems.

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### A shifted complex global Lanczos method and the quasi-minimal residual variant for the Stein-conjugate matrix equation X+AX¯B=C

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

- Computer ScienceNumerical Algorithms
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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…

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