Some Hyperbolic Iterative Methods for Linear Systems
Joint Authors
Kamalvand, M. Ghasemi
Asil, K. Niazi
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-01-07
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
The indefinite inner product defined by J=diagj1,…,jn, jk∈−1,+1, arises frequently in some applications, such as the theory of relativity and the research of the polarized light.
This indefinite scalar product is referred to as hyperbolic inner product.
In this paper, we introduce three indefinite iterative methods: indefinite Arnoldi’s method, indefinite Lanczos method (ILM), and indefinite full orthogonalization method (IFOM).
The indefinite Arnoldi’s method is introduced as a process that constructs a J-orthonormal basis for the nondegenerated Krylov subspace.
The ILM method is introduced as a special case of the indefinite Arnoldi’s method for J-Hermitian matrices.
IFOM is mentioned as a process for solving linear systems of equations with J-Hermitian coefficient matrices.
Finally, by providing numerical examples, the FOM, IFOM, and ILM processes have been compared with each other in terms of the required time for solving linear systems and also from the point of the number of iterations.
American Psychological Association (APA)
Asil, K. Niazi& Kamalvand, M. Ghasemi. 2020. Some Hyperbolic Iterative Methods for Linear Systems. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1174619
Modern Language Association (MLA)
Asil, K. Niazi& Kamalvand, M. Ghasemi. Some Hyperbolic Iterative Methods for Linear Systems. Journal of Applied Mathematics No. 2020 (2020), pp.1-8.
https://search.emarefa.net/detail/BIM-1174619
American Medical Association (AMA)
Asil, K. Niazi& Kamalvand, M. Ghasemi. Some Hyperbolic Iterative Methods for Linear Systems. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1174619
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174619