Backward error analysis and inverse eigenvalue problems for Hankel and Symmetric-Toeplitz structures

Sk. Safique Ahmad and Prince Kanhya

Applied Mathematics and Computation, 2021, vol. 406, issue C

Abstract: This work deals with the study of structured backward error analysis of Hankel and symmetric-Toeplitz matrix pencils. These structured matrix pencils belong to the class of symmetric matrix pencils with some additional properties that a symmetric matrix pencil does not have in general. The perturbation analysis of these two structures is discussed one by one to depict the additional properties explicitly. Present work shows the entrywise structured perturbation of matrix pencils in Frobenius norm such that the specified eigenpairs become exact eigenpairs of an appropriately perturbed matrix pencil. The framework used here maintains the sparsity in the perturbation of the above-structured matrix pencils. Further, the backward error results help for solving a variety of inverse eigenvalue problems.

Keywords: Matrix pencil; Backward error; Hankel generalized eigenvalue problems; Symmetric-Toeplitz generalized eigenvalue problem; Generalized inverse eigenvalue problem (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003775

DOI: 10.1016/j.amc.2021.126288

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