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BIT Numerical Mathematics

Erschienen in:

19.06.2021

Structured perturbation analysis for an infinite size quasi-Toeplitz matrix equation with applications

verfasst von: Hyun-Min Kim, Jie Meng

Erschienen in: BIT Numerical Mathematics | Ausgabe 3/2021

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Abstract

This paper is concerned with the generalized Sylvester equation \(AXB+CXD=E\), where A, B, C, D, E are infinite size matrices with a quasi Toeplitz structure, that is, a semi-infinite Toeplitz matrix plus an infinite size compact correction matrix. Under certain conditions, an equation of this type has a unique solution possessing the same structure as the coefficient matrix does. By separating the analysis on the Toeplitz part with that on the correction part, we provide perturbation results that cater to the particular structure in the coefficient matrices. We show that the Toeplitz part is well-conditioned if the whole problem, without considering the structure, is well-conditioned. Perturbation results that are illustrated through numerical examples are applied to equations arising in the analysis of a Markov process and the 2D Poisson problem.

Vorheriger Artikel Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators

Nächster Artikel A generalized Fourier–Hermite method for the Vlasov–Poisson system

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Titel: Structured perturbation analysis for an infinite size quasi-Toeplitz matrix equation with applications
verfasst von: Hyun-Min Kim
Jie Meng
Publikationsdatum: 19.06.2021
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 3/2021
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-021-00847-2

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