On the Kronecker Structure of linearization of Cubic Two-Parameter Eigenvalue Problems

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Published: Mar 28, 2025
DOI: https://doi.org/10.22452/mjs.vol44no1.9
Keywords:
Cubic two-parameter eigenvalue problem, Linear two-parameter eigenvalueproblem, linearization, matrix polynomial.

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Niranjan Bora
Department of Mathematics, Dibrugarh University Institute of Engineering and Technology Assam-786004, INDIA.
https://orcid.org/0000-0002-3729-5848
Bharati Borgohain
Department of Mathematics, Dibrugarh University, Assam-786004, INDIA.
https://orcid.org/0009-0007-3475-5267

Abstract

Linearization is a classical approach to study matrix polynomial of the form P(lambda)=Sum lambdaj Aj, where A j 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.

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How to Cite
Bora, N., & Borgohain, B. (2025). On the Kronecker Structure of linearization of Cubic Two-Parameter Eigenvalue Problems. Malaysian Journal of Science, 44(1), 70–86. https://doi.org/10.22452/mjs.vol44no1.9
Issue
Vol 44 No 1 (2025): March 2025
Section
Original Articles
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