The eigenvalues for preconditioned system in interior points method for quadratic programming
Other Title(s)
القيم الذاتية للنظام المكيف في طريقة النقاط الداخلية للبرامج التربيعية
Author
Source
Damascus University Journal for the Basic Sciences
Issue
Vol. 31, Issue 2 (31 Dec. 2015), pp.13-24, 12 p.
Publisher
Publication Date
2015-12-31
Country of Publication
Syria
No. of Pages
12
Main Subjects
Abstract EN
Krylov subspace methods are one of the strongest iterative approach, which are used to solve large scale linear systems.
These methods are based on a general type of projection process.
As at each iteration of interior points method (IPM) at least one linear system has to be solved, where the main computational effort of IPMs consist in the computational of these linear systems.
Therefore, we suggest to use Krylov subspace methods to solve these linear systems.
In the paper (Al-Jeiroudi, 2011), it has been introduced a new preconditioner for the augmented system, which arises from IPM for quadratic programming.
Since, in most cases Krylov subspace methods require preconditioner to improve the global convergence.
The eigenvalues play critical role in the convergence analysis of Krylov subspace methods.
Therefore, in this paper we are going to focus our attention to study the eigenvalues of the preconditioned augmented system, which are preconditioned by the previous preconditioner.
In this paper, we introduced new theorem, which studies the eigenvalues behaviour of the preconditioned system, and we show that, the eigenvalues are bounded away from zero.
In addition, they are equal to one exactly or one plus a positive number.
Moreover, they are well clustered and consequently this play an important role in the convergence speed
American Psychological Association (APA)
al-Jirudi, Ghsun. 2015. The eigenvalues for preconditioned system in interior points method for quadratic programming. Damascus University Journal for the Basic Sciences،Vol. 31, no. 2, pp.13-24.
https://search.emarefa.net/detail/BIM-873870
Modern Language Association (MLA)
al-Jirudi, Ghsun. The eigenvalues for preconditioned system in interior points method for quadratic programming. Damascus University Journal for the Basic Sciences Vol. 31, no. 2 (2015), pp.13-24.
https://search.emarefa.net/detail/BIM-873870
American Medical Association (AMA)
al-Jirudi, Ghsun. The eigenvalues for preconditioned system in interior points method for quadratic programming. Damascus University Journal for the Basic Sciences. 2015. Vol. 31, no. 2, pp.13-24.
https://search.emarefa.net/detail/BIM-873870
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 23-24
Record ID
BIM-873870