Random points are optimal for the approximation of Sobolev functions

Polynomial Approximation of Functions in Sobolev Spaces

Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hubert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer o...

Optimal Approximation of Functions

developing a pattern based on speech acts and language functions for developing materials for the course “ the study of islamic texts translation”

هدف پژوهش حاضر ارائه ی الگویی بر اساس کنش گفتار و کارکرد زبان برای تدوین مطالب درس "بررسی آثار ترجمه شده ی اسلامی" می باشد. در الگوی جدید، جهت تدوین مطالب بهتر و جذاب تر، بر خلاف کتاب-های موجود، از مدل های سطوح گفتارِ آستین (1962)، گروه بندی عملکردهای گفتارِ سرل (1976) و کارکرد زبانیِ هالیدی (1978) بهره جسته شده است. برای این منظور، 57 آیه ی شریفه، به صورت تصادفی از بخش-های مختلف قرآن انتخاب گردید...

Nonlinear Approximation of Random Functions

Given an orthonormal basis and a certain class X of vectors in a Hilbert space H, consider the following nonlinear approximation process: approach a vector x ∈ X by keeping only its N largest coordinates, and let N go to infinity. In this paper, we study the accuracy of this process in the case where H = L(I), and we use either the trigonometric system or a wavelet basis to expand this space. T...

On approximation of functions from Sobolev spaces on metric graphs

Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. In particular, we show that the approximation numbers an of the embedding operator of the Sobolev space L (G) on a graph G of finite length |G| into the space L(G, μ), where μ is an arbitrary finite Borel measure on G, satisfy the inequality an ≤ |G| 1/p′μ(G)1/pn−1, 1 < p < ∞....