A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis

The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p = 45 requiring 10 matrix by matrix multiplications per iteration is proposed for computing the Moore–Penrose inverse of a nonzero matrix of rank = r . Convergence and a...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2019; no. 1; pp. 1 - 14
Main Authors: Buranay, Suzan C., Iyikal, Ovgu C.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 20.07.2019
Springer Nature B.V
SpringerOpen
Subjects:
Aircraft industry
Algorithms
Analysis
Applications of Mathematics
Convergence
Error analysis
Ill posed problems
Image restoration
Image restoration problem
Iterative methods
Least squares
Linear least squares problems
Mathematics
Mathematics and Statistics
Matrix algorithms
Moore–Penrose inverse
Perturbation error analysis
Perturbation methods
Predictor-corrector methods
Recent Advances in General Inequalities on Pure & Applied Mathematics and Related Areas
Perturbation error analysis
Moore–Penrose inverse
Image restoration problem
65F30
65F20
Linear least squares problems
Matrix algorithms
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p = 45 requiring 10 matrix by matrix multiplications per iteration is proposed for computing the Moore–Penrose inverse of a nonzero matrix of rank = r . Convergence and a priori error analysis of the proposed method are given. Secondly, the numerical solution to the general linear least squares problems by an algorithm using the proposed method and the perturbation error analysis are provided. Furthermore, experiments are conducted on the ill-posed problem of one-dimensional image restoration and on some test problems from Harwell–Boeing collection. Obtained numerical results show the applicability, stability, and the estimated order of convergence of the proposed method.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-019-2154-z