Zobrazeno 1 - 10
of 37
pro vyhledávání: '"Shadrin, Alexei"'
Autor:
Adcock, Ben, Shadrin, Alexei
We consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is generally impo
Externí odkaz:
http://arxiv.org/abs/2110.03755
We study the quantity $$ \tau_{n,k}:=\frac{|T_n^{(k)}(\omega_{n,k})|}{T_n^{(k)}(1)}\,, $$ where $T_n$ is the Chebyshev polynomial of degree $n$, and $\omega_{n,k}$ is the rightmost zero of $T_n^{(k+1)}$. Since the absolute values of the local maxima
Externí odkaz:
http://arxiv.org/abs/1710.06120
Autor:
Nikolov, Geno, Shadrin, Alexei
Let $w_\alpha(t) := t^{\alpha}\,e^{-t}$, where $\alpha > -1$, be the Laguerre weight function, and let $\|\cdot\|_{w_\alpha}$ be the associated $L_2$-norm, $$ \|f\|_{w_\alpha} = \left\{\int_{0}^{\infty} |f(x)|^2 w_\alpha(x)\,dx\right\}^{1/2}\,. $$ By
Externí odkaz:
http://arxiv.org/abs/1705.03824
Autor:
Nikolov, Geno, Shadrin, Alexei
Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where $\lambda > -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$ \|f\|_{w_{\lambda}} = \left\{\int_{-1}^1 |f(x)|^2 w_{\lambda}(x)\,dx\righ
Externí odkaz:
http://arxiv.org/abs/1701.07682
Autor:
Nikolov, Geno, Shadrin, Alexei
Publikováno v:
In Journal of Approximation Theory November 2021 271
We consider the problem of approximating an analytic function on a compact interval from its values at $M+1$ distinct points. When the points are equispaced, a recent result (the so-called impossibility theorem) has shown that the best possible conve
Externí odkaz:
http://arxiv.org/abs/1610.04769
Autor:
Nikolov, Geno, Shadrin, Alexei
Let $w_{\alpha}(t)=t^{\alpha}\,e^{-t}$, $\alpha>-1$, be the Laguerre weight function, and $|\cdot|_{w_\alpha}$ denote the associated $L_2$-norm, i.e., $$ | f|_{w_\alpha}:=\Big(\int_{0}^{\infty}w_{\alpha}(t)| f(t)|^2\,dt\Big)^{1/2}. $$ Denote by ${\ca
Externí odkaz:
http://arxiv.org/abs/1605.02508
Let $w_{\lambda}(t)=(1-t^2)^{\lambda-1/2}$, $\lambda>-1/2$, be the Gegenbauer weight function, and $\Vert\cdot\Vert$ denote the associated $L_2$-norm, i.e., $$ \Vert f\Vert:=\Big(\int_{-1}^{1}w_{\lambda}(t)\vert f(t)\vert^2\,dt\Big)^{1/2}. $$ Denote
Externí odkaz:
http://arxiv.org/abs/1510.03265
Autor:
Adcock, Ben1 (AUTHOR), Shadrin, Alexei2 (AUTHOR) a.shadrin@damtp.cam.ac.uk
Publikováno v:
Constructive Approximation. Apr2023, Vol. 57 Issue 2, p257-294. 38p.
Autor:
Passenbrunner, Markus, Shadrin, Alexei
The main result of this paper is a proof that, for any $f \in L_1[a,b]$, a sequence of its orthogonal projections $(P_{\Delta_n}(f))$ onto splines of order $k$ with arbitrary knots $\Delta_n$, converges almost everywhere provided that the mesh diamet
Externí odkaz:
http://arxiv.org/abs/1308.4824