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

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  • Ahmad, Sk. Safique
  • Kanhya, Prince

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.

Suggested Citation

  • Ahmad, Sk. Safique & Kanhya, Prince, 2021. "Backward error analysis and inverse eigenvalue problems for Hankel and Symmetric-Toeplitz structures," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    • Handle: RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003775
    DOI: 10.1016/j.amc.2021.126288
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    References listed on IDEAS

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    1. Zhang, Hairui & Yuan, Yongxin, 2019. "Generalized inverse eigenvalue problems for Hermitian and J-Hamiltonian/skew-Hamiltonian matrices," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 609-616.
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