Academic Journal
On the Kronecker Structure of linearization of Cubic Two-Parameter Eigenvalue Problems
| Title: | On the Kronecker Structure of linearization of Cubic Two-Parameter Eigenvalue Problems |
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| Authors: | Bora, Niranjan, Borgohain, Bharati |
| Source: | Malaysian Journal of Science (MJS); Vol 44 No 1 (2025): March 2025; 70-86 ; 2600-8688 ; 1394-3065 |
| Publisher Information: | Faculty of Science, Universiti Malaya |
| Publication Year: | 2025 |
| Subject Terms: | Cubic two-parameter eigenvalue problem, Linear two-parameter eigenvalueproblem, linearization, matrix polynomial |
| Description: | Linearization is a classical approach to study matrix polynomial of the form P(lambda)=Sum lambdaj Aj, where Aj Cnxn . It converts into a matrix pencil of the form L(lambda)=A+lambda B of high dimension, where A and B are matrices over C , and lambda is the spectral parameter. In this paper we consider Cubic two-parameter eigenvalue problems ( CTEP) and study three different linearization process of the problem. Usinglinearization techniques, CTEP is first converted into a linear two-parameter eigenvalue problem(L2EP) of coefficient matrices of different sizes. The main advantage of these linearizations lies in the fact that, after transforming them into suitable linearized forms, existing numerical techniques for linear multiparameter eigenvalue problems (LMEP) can be applied to CTEP without solving the original problem. While solving CTEP by formulating suitable linearizations, several transformations are generally used. In the current paper, it is also intended to report on these transformations, which have not been studied completely due to the complexity of their Kronecker structures. |
| Document Type: | article in journal/newspaper |
| File Description: | application/pdf |
| Language: | English |
| Relation: | https://ejournal.um.edu.my/index.php/index/article/view/45991/18200; https://ejournal.um.edu.my/index.php/index/article/view/45991 |
| DOI: | 10.22452/mjs.vol44no1.9 |
| Availability: | https://ejournal.um.edu.my/index.php/index/article/view/45991 https://doi.org/10.22452/mjs.vol44no1.9 |
| Rights: | Copyright (c) 2025 Malaysian Journal of Science ; https://creativecommons.org/licenses/by-nc/4.0 |
| Accession Number: | edsbas.9275F745 |
| Database: | BASE |
| DOI: | 10.22452/mjs.vol44no1.9 |
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