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A generalized inverse eigenvalue problem and m-functions

Behera, KK (2021) A generalized inverse eigenvalue problem and m-functions. In: Linear Algebra and Its Applications, 622 . pp. 46-65.

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Official URL: https://doi.org/10.1016/j.laa.2021.03.025


In this manuscript, a generalized inverse eigenvalue problem is considered that involves a linear pencil (zJ0,n�H0,n) of (n+1) by (n+1) matrices arising in the theory of rational interpolation and biorthogonal rational functions. In addition to the reconstruction of the Hermitian matrix H0,n, characterizations of the rational functions that are components of the prescribed eigenvectors are given. A condition concerning the positive-definiteness of J0,n which is often an assumption in the direct problem is also isolated. Further, the reconstruction of H0,n is viewed through the inverse of the pencil (zJ0,n�H0,n) which involves the concept of m-functions. © 2021 Elsevier Inc.

Item Type: Journal Article
Publication: Linear Algebra and Its Applications
Publisher: Elsevier Inc.
Additional Information: The copyright for this article belongs to Author
Keywords: Inverse problems; Matrix algebra; Rational functions, Biorthogonal; Condition; Generalized inverse eigenvalue problems; Hermitian matrices; Linear pencil; M-function; matrix; Positive definiteness; Rational interpolation; Tridiagonal matrices, Eigenvalues and eigenfunctions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 Jul 2021 10:19
Last Modified: 19 Jul 2021 10:19
URI: http://eprints.iisc.ac.in/id/eprint/68702

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