On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices
We consider the problem of convergence to zero of matrix products AnBn⋯A1B1 with factors from two sets of matrices, Ai∈A and Bi∈B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix p...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2018/9216760 |
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| author | Victor Kozyakin |
| author_facet | Victor Kozyakin |
| author_sort | Victor Kozyakin |
| collection | DOAJ |
| description | We consider the problem of convergence to zero of matrix products AnBn⋯A1B1 with factors from two sets of matrices, Ai∈A and Bi∈B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix products AnBn⋯A1B1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, AnBn⋯A1B1≤Cλn, where the constants C>0 and λ∈(0,1) do not depend on the sequence {Ai} and the corresponding sequence {Bi}. Other problems of this kind are discussed and open questions are formulated. |
| format | Article |
| id | doaj-art-4cf671bc4c75458d9b53f17ee0aec4fb |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-4cf671bc4c75458d9b53f17ee0aec4fb2025-02-03T01:29:01ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2018-01-01201810.1155/2018/92167609216760On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of MatricesVictor Kozyakin0Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoi Karetny Lane 19, Moscow 127051, RussiaWe consider the problem of convergence to zero of matrix products AnBn⋯A1B1 with factors from two sets of matrices, Ai∈A and Bi∈B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix products AnBn⋯A1B1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, AnBn⋯A1B1≤Cλn, where the constants C>0 and λ∈(0,1) do not depend on the sequence {Ai} and the corresponding sequence {Bi}. Other problems of this kind are discussed and open questions are formulated.http://dx.doi.org/10.1155/2018/9216760 |
| spellingShingle | Victor Kozyakin On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices Discrete Dynamics in Nature and Society |
| title | On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices |
| title_full | On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices |
| title_fullStr | On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices |
| title_full_unstemmed | On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices |
| title_short | On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices |
| title_sort | on convergence of infinite matrix products with alternating factors from two sets of matrices |
| url | http://dx.doi.org/10.1155/2018/9216760 |
| work_keys_str_mv | AT victorkozyakin onconvergenceofinfinitematrixproductswithalternatingfactorsfromtwosetsofmatrices |