The Order of Comonotone Approximation of Differentiable Periodic Functions
نویسندگان
چکیده
Let Δ(1)(Y ) be a set of all 2
منابع مشابه
gH-differentiable of the 2th-order functions interpolating
Fuzzy Hermite interpolation of 5th degree generalizes Lagrange interpolation by fitting a polynomial to a function f that not only interpolates f at each knot but also interpolates two number of consecutive Generalized Hukuhara derivatives of f at each knot. The provided solution for the 5th degree fuzzy Hermite interpolation problem in this paper is based on cardinal basis functions linear com...
متن کاملNearly Comonotone Approximation
We discuss the degree of approximation by polynomials of a function f that is piecewise monotone in ?1; 1]. We would like to approximate f by polynomials which are comonotone with it. We show that by relaxing the requirement for comonotonicity in small neighborhoods of the points where changes in monotonicity occur and near the endpoints, we can achieve a higher degree of approximation. We show...
متن کاملNearly Comonotone Approximation Ii
When we approximate a continuous function f which changes its monotonicity nitely many, say s times, in ?1; 1], we wish sometimes that the approximating polynomials follow these changes in monotonicity. However, it is well known that this requirement restricts very much the degree of approximation that the polynomials can achieve, namely, only the rate of ! 2 (f; 1=n) and even this not with a c...
متن کاملOrder-preserving derivative approximation with periodic radial basis functions
In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis function (RBF) interpolation. Given a target function sampled on some node set, an approximation of the m derivative is obtained by m successive applications of the operator “interpolate, then differentiate” this process is known in the spline com...
متن کاملApproximation of infinitely differentiable multivariate functions is intractable
We prove that L∞-approximation of C ∞-functions defined on [0, 1]d is intractable and suffers from the curse of dimensionality. This is done by showing that the minimal number of linear functionals needed to obtain an algorithm with worst case error at most ε ∈ (0, 1) is exponential in d. This holds despite the fact that the rate of convergence is infinite.
متن کاملذخیره 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: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-05717-y