Related papers: Iterates of Markov operators and their limits
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Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…
We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete- time linear systems. We mainly focus on the so-called Krasnoselskij-Mann iteration x(k+1) = ( 1 - \alpha(k) ) x(k) + \alpha(k) A…
Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…
Using straightforward linear algebra we derive response operators describing the impact of small perturbations to finite state Markov processes. The results can be used for studying empirically constructed - e.g. from observations or…
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We associate to each iterated function system consisting of phi-max-contractions an operator (on the space of continuous functions from the shift space on the metric space corresponding to the system) having a unique fixed point whose image…
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A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over a infinite state space can be identified by a…
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