The DOI matches its Crossref record; 117 of the 117 references it cites were found in a registry or an index.
Recent computational developments in Krylov subspace methods for linear systems
Abstract
Many advances in the development of Krylov subspace methods for the iterative solution of linear systems during the last decade and a half are reviewed. These new developments include different versions of restarted, augmented, deflated, flexible, nested, and inexact methods. Also reviewed are methods specifically tailored to systems with special properties such as special forms of symmetry and those depending on one or more parameters. Copyright © 2006 John Wiley & Sons, Ltd.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Lecture Notes in Computer Science 1205
(1999) · Industrial Robot: An International Journal · doi:10.1108/ir.1999.04926fae.001 · Cited by 38,662
Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Iterative Methods for Sparse Linear Systems
Saad, Y. (2003) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718003 · Cited by 13,790
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
Saad, Y., & Schultz, M. H. (1986) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0907058 · Cited by 11,154
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 10,280
Methods of conjugate gradients for solving linear systems
Hestenes, M. R., & Stiefel, E. (1952) · Journal of Research of the National Bureau of Standards · doi:10.6028/jres.049.044 · Cited by 8,132
Golub, G. H., & Loan, C. F. V. (1996) · Johns Hopkins University Press eBooks · Cited by 6,027
van der Vorst, H. A. (1992) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0913035 · Cited by 5,308
Linear and nonlinear programming.
(1986) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(86)90092-3 · Cited by 4,805
Metadata
- Authors
- Simoncini, V., & Szyld, D. B.
- Venue
- Numerical Linear Algebra with Applications
- Publisher
- Wiley
- Published
- 2006-10-09
- Volume
- 14
- Issue
- 1
- Pages
- 1-59
- ISSN
- 1070-5325 (ISSN-L)
- 1099-1506
- OpenAlex
- W2074780612
- Cited by
- 375
- References
- 117
- FWCI
- 16.74
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Recent computational developments in Krylov subspace methods for linear systems. https://app.cochat.ai/papers/10.1002/nla.499
- The paper
- Simoncini, V., & Szyld, D. B. (2007). Recent computational developments in Krylov subspace methods for linear systems. Numerical Linear Algebra with Applications. https://doi.org/10.1002/nla.499
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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.
