The DOI matches its Crossref record.
Computing integrals involving the matrix exponential
Abstract
A new algorithm for computing integrals involving the matrix exponential is given. The method employs diagonal Padé approximation with scaling and squaring. Rigorous truncation error bounds are given and incorporated in a Fortran subroutine. The computational aspects of this program are discussed and compared with existing techniques.
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
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later
Moler, C., & Van Loan, C. (2003) · SIAM Review · doi:10.1137/s00361445024180 · Cited by 2,357
Kalman filtering for relative spacecraft attitude and position estimation
Kim, S.-G., Crassidis, J. L., Cheng, Y., Fosbury, A. M., & Junkins, J. L. (2007) · Journal of Guidance Control and Dynamics · doi:10.2514/1.22377 · Cited by 320
The 2017 IEEE International Conference on Fuzzy Systems
(2016) · IEEE Computational Intelligence Magazine · doi:10.1109/mci.2016.2545826 · Cited by 308
Xing, Y., Cao, X., Zhang, S., Guo, H., & Wang, F. (2010) · Acta Astronautica · doi:10.1016/j.actaastro.2010.04.002 · Cited by 71
Chen, F., Garnier, H., & Gilson, M. (2015) · Journal of Process Control · doi:10.1016/j.jprocont.2014.10.003 · Cited by 68
Metadata
- Authors
- Van Loan, C.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1978-06
- Volume
- 23
- Issue
- 3
- Pages
- 395-404
- ISSN
- 0018-9286 (ISSN-L)
- OpenAlex
- W2156464932
- Cited by
- 832
- References
- 0
- FWCI
- 4.14
- 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: Computing integrals involving the matrix exponential. https://app.cochat.ai/papers/10.1109/tac.1978.1101743
- The paper
- Van Loan, C. (1978). Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.1978.1101743
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.
