.png){kind=icon}
.png){kind=icon}
Return
Splitting-base d randomize d iterative methods for solving indefinite least squares problem
.png){kind=icon}
OA
AI
DOI：10.1016/j.amc.2023.127892.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose a simple and effective splitting (SP) method according to its own structure, and prove that it converges for any initial value. Further, to avoid implementing some matrix multiplications and calculating the inverse of large matrix, and considering the acceleration and efficiency of the randomized strategy, we de-velop two randomized iterative methods on the basis of the SP method as well as the randomized Kaczmarz, Gauss-Seidel and coordinate descent methods, and describe their convergence properties. Numerical results show that our three methods all have quite de-cent performance in both computing time and iteration numbers compared with the latest iterative method of the ILS problem, and also demonstrate that the two randomized meth-ods indeed yield significant acceleration in terms of computing time. (c) 2023 Elsevier Inc. All rights reserved.
Keywords:
Indefinite least squares problem
Splitting method
Randomized method
Kaczmarz
Gauss-Seidel
Coordinate descent
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
3.4
Papers:
2.3W
Citations:
3.3W