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2020 Some Hyperbolic Iterative Methods for Linear Systems
K. Niazi Asil, M. Ghasemi Kamalvand
J. Appl. Math. 2020: 1-8 (2020). DOI: 10.1155/2020/9874162


The indefinite inner product defined by J = diag j 1 , , j n , j k 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.


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K. Niazi Asil. M. Ghasemi Kamalvand. "Some Hyperbolic Iterative Methods for Linear Systems." J. Appl. Math. 2020 1 - 8, 2020.


Received: 18 October 2019; Revised: 30 November 2019; Accepted: 3 December 2019; Published: 2020
First available in Project Euclid: 14 May 2020

zbMATH: 07165634
MathSciNet: MR4053176
Digital Object Identifier: 10.1155/2020/9874162

Rights: Copyright © 2020 Hindawi


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