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Transient Response in Matrix Discrete-Time Linear Systems

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Resumo:The behavior of trajectories of multidimensional linear discrete-time systems with nonzero initial conditions is considered in two cases as follows. The first case is the systems with infinite degree of stability (the processes of a finite duration); the second case is the stable systems with a spectral radius close to 1. It is demonstrated that in both cases, large deviations of the trajectories from the equilibrium may occur. These results are applied to accelerated unconstrained optimization methods (such as the Heavy-ball method) for explaining the nonmonotonic behavior of the methods, which is observed in practice.
Autores principais:Polyak, Boris
Outros Autores:Smirnov, Georgi
Assunto:Discrete-time systems Transient response Stability Large deviations Infinite degree of stability Multidimensional systems Heavy-ball method Ciências Naturais::Matemáticas
Ano:2019
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade do Minho
Idioma:inglês
Origem:RepositóriUM - Universidade do Minho

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