37 citations · 110 across the 24 of their papers we have counts for
3 papers · 1 filter
Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models
Gerlind Plonka, Yannick Riebe, Yurii Kolomoitsev
We analyze the structure of a one-dimensional deep ReLU neural network (ReLU DNN) in comparison to the model of continuous piecewise linear (CPL) spline functions with arbitrary kn…
Sparse grid approximation in weighted Wiener spaces
Yurii Kolomoitsev, Tetiana Lomako, Segey Tikhonov
We study approximation properties of multivariate periodic functions from weighted Wiener spaces by sparse grids methods constructed with the help of quasi-interpolation operators.…
Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb, Yurii Kolomoitsev +1
To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue c…