A unified approach to uniform real approximation by polynomials with linear restrictions

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Unified Approach to Uniform Real Approximation by Polynomials with Linear Restrictions

Problems concerning approximation of real-valued continuous functions of a real variable by polynomials of degree smaller than n with various linear restrictions have been studied by several authors. This paper is an attempt to provide a unified approach to these problems. In particular, the notion of restricted derivatives approximation is seen to fit into the theory and includes as special ca...

متن کامل

Uniform approximation by (quantum) polynomials

We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson’s Theorem, which gives a nearly-optimal quantitative version of Weierstrass’s Theorem on uniform approximation of continuous functions by polynomials. We provide two proofs, based respectively on quantum counting and on quantum phase estimation.

متن کامل

Uniform approximation by discrete least squares polynomials

We study uniform approximation of differentiable or analytic functions of one or several variables on a compact set K by a sequence of discrete least squares polynomials. In particular, if K satisfies a Markov inequality and we use point evaluations on standard discretization grids with the number of points growing polynomially in the degree, these polynomials provide nearly optimal approximant...

متن کامل

Uniform weighted approximation by positive linear operators

We characterize the functions defined on a weighted space, which are uniformly approximated by a sequence of positive linear operators and we obtain the range of the weights which can be used for uniform approximation. We, also, obtain an estimation of the remainder in terms of the usual modulus of continuity. We give particular results for the Szász-Mirakjan and Baskakov operators. Mathematics...

متن کامل

Approximation by sums of piecewise linear polynomials

We present two partitioning algorithms that allow a sum of piecewise linear polynomials over a number of overlaying convex partitions of the unit cube Ω in Rd to approximate a function f ∈ W 3 p (Ω) with the order N−6/(2d+1) in Lp-norm, where N is the total number of cells of all partitions, which makes a marked improvement over the N−2/d order achievable on a single convex partition. The gradi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Transactions of the American Mathematical Society

سال: 1972

ISSN: 0002-9947

DOI: 10.1090/s0002-9947-1972-0294962-0