Linear equality-constrained least-square problems by generalized QR factorization
DOI:
https://doi.org/10.17268/sel.mat.2021.02.20Keywords:
GQR factorization, linear equality-constrained least square problemsAbstract
The generalized QR factorization, also known as GQR factorization, is a method that simultaneously transforms two matrices A and B in a triangular form. In this paper, we show the application of GQR factorization in solving linear equality-constrained least square problems; in addition, we explain how to use GQR factorization for solving quaternion least-square problems through the matrix representation of quaternions.
References
Anderson E, Bai Z, Dongarra Z. Generalized qr factorization and its applications. Linear Algebra Appl. 1992; 162-164:243-271.
Golub G, Van Loan C. Matrix computations. 4th ed. Baltimore: The Johns Hopkins University Press; 2012.
Hammarling S. The numerical solution of the general Gauss-Markov linear model. In: Durrani, T. et al. editors. Mathematics in Signal Processing. Oxford: Clarendon Press; 1986.
Jia Z, Wei M, Zhao M, Chen Y. A new real structure-preserving quaternion QR algorithm. J. Comput. Appl. Math. 2018; 343:26-48.
Jiang T, Chen L. Algebraic algorithms for least squares problem in quaternionic quantum theory. Comput. Phys. Commun. 2007; 176:481-485.
Jiang T, Cheng X, Ling S. An algebraic technique for total least squares problem in quaternionic quantum theory. Appl. Math. Lett. 2016; 52:58-63.
Jiang T, Jiang Z, Zhang Z. Two novel algebraic techniques for quaternion least squares problems in quaternionic quantum mechanics. Adv. Appl. Clifford Algebr. 2016; 26(1):169-182.
Jiang T, Zhao J, Wei M. A new technique of quaternion equality constrained least squares problem. J. Comput. Appl. Math. 2008; 216(2):509-513.
Ling S, Xu X, Jiang T. Algebraic Method for Inequality Constrained Quaternion Least Squares Problem. Adv. Appl. Clifford Algebr. 2013; 23(4):919-928.
Zeb S, Yousaf M. Updating QR factorization procedure for solution of linear least squares problem with equality constraints. J. Inequal. Appl. 2017; 281:1-17.
Zhang F, Wei M, Li Y, Zhao J. Special least squares solutions of the quaternion matrix equation AX = B with applications. Appl. Math. Comput. 2015; 270:425-433.
Zhdanov A, Gogoleva S. Solving least squares problems with equality constraints based on augmented regularized normal equations. Appl. Math. E-Notes. 2015; 15:218-224.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Selecciones Matemáticas
This work is licensed under a Creative Commons Attribution 4.0 International License.
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.
