The DOI matches its Crossref record.
Estimation of Sparse Jacobian Matrices and Graph Coloring Blems
Abstract
Given a mapping with a sparse Jacobian matrix, we investigate the problem of minimizing the number of function evaluations needed to estimate the Jacobian matrix by differences. We show that this problem can be attacked as a graph coloring problem and that this approach leads to very efficient algorithms. The behavior of these algorithms is studied and, in particular, we prove that two of the algorithms are optimal for band graphs. We also present numerical evidence which indicates that these two algorithms are nearly optimal on practical problems.
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
Cited by
Cross-depth analysis of marine bacterial networks suggests downward propagation of temporal changes
Cram, J. A., Xia, L. C., Needham, D. M., Sachdeva, R., Sun, F., & Fuhrman, J. A. (2015) · The ISME Journal · doi:10.1038/ismej.2015.76 · Cited by 133
Metadata
- Authors
- Coleman, T. F., & Moré, J. J.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1983-02
- Volume
- 20
- Issue
- 1
- Pages
- 187-209
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W1995561370
- Cited by
- 468
- References
- 0
- FWCI
- 8.97
- 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: Estimation of Sparse Jacobian Matrices and Graph Coloring Blems. https://app.cochat.ai/papers/10.1137/0720013
- The paper
- Coleman, T. F., & Moré, J. J. (1983). Estimation of Sparse Jacobian Matrices and Graph Coloring Blems. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0720013
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.
