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Non-local Nonlinear Perturbation Analysis for a Nonlinear Matrix Equation Arising in Tree-Like Stochastic Processes

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Advanced Computing in Industrial Mathematics (BGSIAM 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 961))

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Abstract

For a nonlinear matrix equation arising in tree-like stochastic processes in [1] norm-wise, mixed and component-wise condition numbers, as well as local perturbation bounds are formulated and norm-wise non-local residual bounds are derived. The local bounds are valid only asymptotically. The exigence to be small enough for the perturbations in the data in order to ensure sufficient accuracy of the local bound is an disadvantage of the local bound which is overcome in the non-local perturbation bound. As a continuation of the previous results, in this paper a non-local perturbation bound for the solution to the nonlinear matrix equation arising in tree-like stochastic processes is formulated using the techniques of Fréchet derivatives and the methods of Lyapunov majorants and fixed-point principles. The non-local bound is more pessimistic than the local bound, but it is formulated for data perturbations included in a given a priori prescribed domain which guarantees the existence of the solution to the perturbed equation in a neighborhood of the exact solution. The perturbation bound is an obligatory element when computing the solution of an equation.

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Authors and Affiliations

  1. Institute of Information and Communication Technologies - BAS, Akad. G. Bonchev, Street Bl. 2, Sofia, Bulgaria

    Vera Angelova

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  1. Vera Angelova
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Correspondence to Vera Angelova .

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Editors and Affiliations

  1. Institute of Information and Communication Technologies and Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Science, Sofia, Bulgaria

    Hristo Kostadinov

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Science, Sofia, Bulgaria

    Elena Lilkova

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Angelova, V. (2021). Non-local Nonlinear Perturbation Analysis for a Nonlinear Matrix Equation Arising in Tree-Like Stochastic Processes. In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2018. Studies in Computational Intelligence, vol 961. Springer, Cham. https://doi.org/10.1007/978-3-030-71616-5_3

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