Backward Error of Approximate Eigenelements Of a Regular Rational Matrix
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Department of Mathematics, Sikkim University, Gangtok-737102, Sikkim ,IN
Namita Behera
DOI:
https://doi.org/10.18311/jims/2024/31241Keywords:
Rational matrix, Realization, Matrix polynomial, Eigenvalue, Eigenvector, Fiedler pencil, Linearization, Backward error.Abstract
We consider a minimal realization of a rational matrix. We perturb all the coefficients of matrix polynomial and some coefficients from the realization part present in the realization form of rational matrix. We derive explicit computable formulae for backward error of approximate eigenvalues and eigenpairs of regular rational matrix. We also determine minimal perturbations for all the coefficients of matrix polynomial and some coefficients from the realization part for which approximate eigenvalues are exact eigenvalues of the perturbed rational matrix.
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Copyright (c) 2024 Namita Behera
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023-01-20
Published 2024-01-01
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