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Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
Abstract
Recently the Conjugate Gradients-Squared (CG-S) method has been proposed as an attractive variant of the Bi-Conjugate Gradients (Bi-CG) method. However, it has been observed that CG-S may lead to a rather irregular convergence behaviour, so that in some cases rounding errors can even result in severe cancellation effects in the solution. In this paper, another variant of Bi-CG is proposed which does not seem to suffer from these negative effects. Numerical experiments indicate also that the new variant, named Bi-CGSTAB, is often much more efficient than CG-S.
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Citations
Cited by
Mayer, K. U., Frind, E. O., & Blowes, D. W. (2002) · Water Resources Research · doi:10.1029/2001wr000862 · Cited by 568
Potse, M., Dube, B., Richer, J., Vinet, A., & Gulrajani, R. M. (2006) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2006.880875 · Cited by 470
Variational optimization algorithms for uniform matrix product states
Zauner-Stauber, V., Vanderstraeten, L., Fishman, M. T., Verstraete, F., & Haegeman, J. (2018) · Physical Review B · doi:10.1103/physrevb.97.045145 · Cited by 270
Self-Adapting Linear Algebra Algorithms and Software
Demmel, J., Dongarra, J., Eijkhout, V., Fuentes, E., Petitet, A., Vuduc, R., Whaley, R. C., & Yelick, K. (2005) · Proceedings of the IEEE · doi:10.1109/jproc.2004.840848 · Cited by 204
Exact analysis of TTL cache networks
Berger, D. S., Gland, P., Singla, S., & Ciucu, F. (2014) · Performance Evaluation · doi:10.1016/j.peva.2014.07.001 · Cited by 95
Metadata
- Authors
- van der Vorst, H. A.
- Venue
- SIAM Journal on Scientific and Statistical Computing
- Published
- 1992-03
- Volume
- 13
- Issue
- 2
- Pages
- 631-644
- ISSN
- 0196-5204 (ISSN-L)
- 2168-3417
- OpenAlex
- W2155216327
- Cited by
- 5,308
- References
- 0
- FWCI
- 96.79
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. https://app.cochat.ai/papers/10.1137/0913035
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- van der Vorst, H. A. (1992). Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems. SIAM Journal on Scientific and Statistical Computing. https://doi.org/10.1137/0913035
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
