The DOI matches its Crossref record.
Extensions and applications of the Householder algorithm for solving linear least squares problems
Open accessAbstract
The mathematical and numerical least squares solution of a general linear system of equations is discussed. Perturbation and differentiability theorems for pseudoinverses are given. Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential processing of data, and processing of block diagonal matrices form a partial list of numerical topics presented.
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
Beamforming: a versatile approach to spatial filtering
Van Veen, B. D., & Buckley, K. M. (1988) · IEEE ASSP Magazine · doi:10.1109/53.665 · Cited by 3,901
Perturbation theory for pseudo-inverses
Wedin, P.-Å. (1973) · BIT · doi:10.1007/bf01933494 · Cited by 346
MIMO Transceiver Design via Majorization Theory
Palomar, D. P., & Jiang, Y. (2007) · Foundations and Trends in Communications and Information Theory · doi:10.1561/0100000018 · Cited by 320
Metadata
- Authors
- Hanson, R. J., & Lawson, C. L.
- Venue
- Mathematics of Computation
- Publisher
- American Mathematical Society (AMS)
- Published
- 1969
- Volume
- 23
- Issue
- 108
- Pages
- 787-812
- ISSN
- 0025-5718 (ISSN-L)
- 1088-6842
- OpenAlex
- W2093149052
- Cited by
- 158
- References
- 0
- FWCI
- 7.14
- Type
- journal article
- Language
- en
- Open access
- bronze
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: Extensions and applications of the Householder algorithm for solving linear least squares problems. https://app.cochat.ai/papers/10.1090/s0025-5718-1969-0258258-9
- The paper
- Hanson, R. J., & Lawson, C. L. (1969). Extensions and applications of the Householder algorithm for solving linear least squares problems. Mathematics of Computation. https://doi.org/10.1090/s0025-5718-1969-0258258-9
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.
