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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Veröffentlicht in:	Journal of inequalities and applications Jg. 2019; H. 1; S. 1 - 14
Hauptverfasser:	Buranay, Suzan C., Iyikal, Ovgu C.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 20.07.2019 Springer Nature B.V SpringerOpen
Schlagworte:	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
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Abstract	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.
AbstractList	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. The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p=45$p=45$ requiring 10 matrix by matrix multiplications per iteration is proposed for computing the Moore–Penrose inverse of a nonzero matrix of rank=r$\operatorname{rank}=r$. 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. Abstract The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p=45 $p=45$ requiring 10 matrix by matrix multiplications per iteration is proposed for computing the Moore–Penrose inverse of a nonzero matrix of rank=r $\operatorname{rank}=r$. 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.
ArticleNumber	203
Author	Iyikal, Ovgu C. Buranay, Suzan C.
Author_xml	– sequence: 1 givenname: Suzan C. orcidid: 0000-0002-3446-1521 surname: Buranay fullname: Buranay, Suzan C. email: suzan.buranay@emu.edu.tr organization: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University – sequence: 2 givenname: Ovgu C. surname: Iyikal fullname: Iyikal, Ovgu C. organization: Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University
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Snippet	The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p = 45 requiring 10 matrix by... The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p=45$p=45$ requiring 10... Abstract The motivation of the present work concerns two objectives. Firstly, a predictor-corrector iterative method of convergence order p=45 $p=45$ requiring...
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SubjectTerms	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
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Title	A predictor-corrector iterative method for solving linear least squares problems and perturbation error analysis
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