Construction of Fiedler-Like Linearizations: An Algorithmic Approach

Ranjan Kumar Das ()
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Ranjan Kumar Das: National Institute of Technology Raipur

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1117-1130

Abstract: Abstract Polynomial and rational eigenvalue problems arise in many applications. Linearization is a widely used method for solving these eigenvalue problems, and with various families of linearizations studied in the literature. Among these, Fiedler-like linearizations, specifically Fiedler pencils with repetition (FPRs) and generalized Fiedler pencils with repetition (GFPRs) are crucial for handling structured matrix polynomials. However, the methods for constructing these linearizations rely on matrix multiplications, which are computationally expensive and difficult to implement. This paper presents operation-free algorithms for constructing FPRs and GFPRs. These algorithms are further extended to construct linearizations for rational eigenvalue problems. We believe that these algorithms have significant potential for developing efficient computational toolboxes.

Keywords: Fiedler pencil; Linearization; Eigenvalue; Matrix polynomial; Rational matrices; 65F15; 15A57; 15A18; 65F35 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00827-0

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