Abstract We present an asymptotic analysis of adaptive methods for L p approximation functions f ∈ C r ([ a , b ]), where $1\le p\le +\infty $ 1 ≤ p + ∞ . The rely on piecewise polynomial interpolation degree − 1 with strategy selecting m sub...

In this paper, we consider the optimal approximations of univariate functions with feed-forward ReLU neural networks. We attempt to answer following questions. For given function and network, what is minimal possible approximation error? How fast does error decrease network size? Is attainable by current training techniques? Theoretically, introduce necessary sufficient conditions for convex fu...

We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed multiscale domain decomposition methods. The diffusion coefficient can arbitrarily rough space time. To construct we consider a compact transfer operator acts on solutions covers full time dimension. then given by left singular vectors operator. prove compactne...

in an axisymmetric co2-n2-h2o gas dynamic laser, let ? denote the intersection of the vertical plane of symmetry with the upper part of the (supersonic) nozzle. to obtain a maximal small signal gain, some authors have tested several families of curves for ?. to find the most general solution for ?, an application of pontryagin’s principle led to the conjuncture that the optimal ? must consist o...