Approximation of differentiable and analytic functions by splines on the torus
| Autor: | Sergio Antonio Tozoni, J.G. Oliveira |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Kernel (set theory) Applied Mathematics 010102 general mathematics Torus Function (mathematics) 01 natural sciences 010101 applied mathematics Sobolev space Distribution (mathematics) Rate of convergence Differentiable function 0101 mathematics Analysis Analytic function Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 493:124456 |
| ISSN: | 0022-247X |
| Popis: | The objective of this article is to construct optimal distribution of data points in the sense of n-widths. We present a concrete method of interpolation using sk-splines which is optimal. For a fixed continuous kernel K on the d-dimensional torus, we consider a generalization of the univariate sk-spline to the torus, associated with the kernel K. An estimate that provides the rate of convergence of a given function by its interpolating sk-splines is proved, in the norm of L q for functions of the type f = K ⁎ φ , where φ ∈ L p and 1 ≤ p ≤ 2 ≤ q ≤ ∞ , 1 / p − 1 / q ≥ 1 / 2 . The rate of convergence is obtained on analogues of Sobolev classes and on classes of analytic functions. These rates have the same order as the respective trigonometric approximations, in the special case p = 1 , q = 2 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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