Linearizations of Cubic Two-Parameter Eigenvalue Problems and Its Vector Space

Authors

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

DOI:

https://doi.org/10.37256/cm.5120243287

Keywords:

2PEP, CTMP, CTEP, kronecker product, linearization, matrix polynomial

Abstract

The paper considers the study of linearization techniques of cubic two-parameter matrix polynomial (CTMP). We analyze vector spaces of linearization of CTMP, namely ansatz vector space and double ansatz vector space. We also consider cubic two-parameter eigenvalue problem (CTEP) to study their linearization classes. A unified framework on linearization of CTMP will be established. The conditions under which a matrix pencil in the ansatz spaces is a linearization of CTMP will also be derived. Moreover, using these linearization techniques, CTEP is first converted into a singular linear two-parameter eigenvalue problem (2PEP) of larger size so that existing numerical method for (2PEP) can be applied.

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Published

2024-03-08

How to Cite

1.
Bora N, Bharati Borgohain BB, Sharma B. Linearizations of Cubic Two-Parameter Eigenvalue Problems and Its Vector Space. Contemp. Math. [Internet]. 2024 Mar. 8 [cited 2024 Oct. 14];5(1):930-48. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3287