scholarly journals Pathwise Error Bounds in Multiscale Variable Splitting Methods for Spatial Stochastic Kinetics

2018 ◽  
Vol 56 (1) ◽  
pp. 469-498 ◽  
Author(s):  
Augustin Chevallier ◽  
Stefan Engblom
Keyword(s):  
Error Bounds ◽  
Splitting Methods ◽  
Variable Splitting ◽  
Stochastic Kinetics

Alternative Variable Splitting Methods to Learn Sum-Product Networks

2017 ◽  
pp. 334-346
Author(s):  
Nicola Di Mauro ◽  
Floriana Esposito ◽  
Fabrizio G. Ventola ◽  
Antonio Vergari
Keyword(s):  
Splitting Methods ◽  
Variable Splitting

scholarly journals Metric Fourier Approximation of Set-Valued Functions of Bounded Variation

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Elena E. Berdysheva ◽  
Nira Dyn ◽  
Elza Farkhi ◽  
Alona Mokhov
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Error Bounds ◽  
Metric Spaces ◽  
Hausdorff Metric ◽  
Dirichlet Kernel ◽  
Partial Sums ◽  
Functions Of Bounded Variation ◽  
Moduli Of Continuity ◽  
Fourier Approximation

AbstractWe introduce and investigate an adaptation of Fourier series to set-valued functions (multifunctions, SVFs) of bounded variation. In our approach we define an analogue of the partial sums of the Fourier series with the help of the Dirichlet kernel using the newly defined weighted metric integral. We derive error bounds for these approximants. As a consequence, we prove that the sequence of the partial sums converges pointwisely in the Hausdorff metric to the values of the approximated set-valued function at its points of continuity, or to a certain set described in terms of the metric selections of the approximated multifunction at a point of discontinuity. Our error bounds are obtained with the help of the new notions of one-sided local moduli and quasi-moduli of continuity which we discuss more generally for functions with values in metric spaces.

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