Least Squares Properties of Generalized Inverses

Least Squares Properties of Generalized Inverses

Year:    2021

Author:    Predrag S. Stanimirović, Mosić Dijana, Yimin Wei

Communications in Mathematical Research , Vol. 37 (2021), Iss. 4 : pp. 421–447

Abstract

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses. As a significant application of the Moore-Penrose inverse, the best approximation solution to linear matrix equations (i.e. both least squares and the minimal norm) is considered. Also, characterizations of least squares solution and solution of minimum norm are given. Basic properties of the Drazin-inverse solution and the outer-inverse solution are present. Motivated by recent research, important least square properties of composite outer inverses are collected.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cmr.2021-0011

Communications in Mathematical Research , Vol. 37 (2021), Iss. 4 : pp. 421–447

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Outer inverse Moore-Penrose inverse DMP inverse core-EP inverse.

Author Details

Predrag S. Stanimirović

Mosić Dijana

Yimin Wei

  1. Generalizations of composite inverses with certain image and/or kernel

    Stanimirović, Predrag S. | Mosić, Dijana | Wei, Yimin

    Applied Mathematics and Computation, Vol. 428 (2022), Iss. P.127155

    https://doi.org/10.1016/j.amc.2022.127155 [Citations: 0]
  2. Matrix and Operator Equations and Applications

    Existence and Representations of Solutions to Some Constrained Systems of Matrix Equations

    Mosić, Dijana | Stanimirović, Predrag S.

    2023

    https://doi.org/10.1007/16618_2023_44 [Citations: 0]
  3. Application of Generalized Inverses in the Minimum-Energy Perfect Control Theory

    Feliks, Tomasz | Hunek, Wojciech Przemysław | Stanimirović, Predrag S.

    IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 53 (2023), Iss. 7 P.4560

    https://doi.org/10.1109/TSMC.2023.3253778 [Citations: 5]
  4. Calculating the Moore–Penrose Generalized Inverse on Massively Parallel Systems

    Stanojević, Vukašin | Kazakovtsev, Lev | Stanimirović, Predrag S. | Rezova, Natalya | Shkaberina, Guzel

    Algorithms, Vol. 15 (2022), Iss. 10 P.348

    https://doi.org/10.3390/a15100348 [Citations: 6]
  5. Alternative algebraic perturbation expressions for the core-EP inverse of a matrix

    Ji, Jun

    Computational and Applied Mathematics, Vol. 43 (2024), Iss. 6

    https://doi.org/10.1007/s40314-024-02841-0 [Citations: 0]
  6. Kaczmarz-type methods for solving matrix equations

    Li, Weiguo | Bao, Wendi | Xing, Lili | Guo, Zhiwei

    International Journal of Computer Mathematics, Vol. 101 (2024), Iss. 7 P.708

    https://doi.org/10.1080/00207160.2024.2372420 [Citations: 0]