Uniform convergence of the greedy algorithm with respect to the Walsh system

Martin Grigoryan

Displaying similar documents to “Uniform convergence of the greedy algorithm with respect to the Walsh system”

The general methods of finding the sum $S_{n}$ for all kinds of series

K. Orlov (1981)

Matematički Vesnik

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Seasonal time-series imputation of gap missing algorithm (STIGMA)

Eduardo Rangel-Heras, Pavel Zuniga, Alma Y. Alanis, Esteban A. Hernandez-Vargas, Oscar D. Sanchez (2023)

Kybernetika

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This work presents a new approach for the imputation of missing data in weather time-series from a seasonal pattern; the seasonal time-series imputation of gap missing algorithm (STIGMA). The algorithm takes advantage from a seasonal pattern for the imputation of unknown data by averaging available data. We test the algorithm using data measured every $10$ minutes over a period of $365$ days during the year 2010; the variables include global irradiance, diffuse irradiance, ultraviolet irradiance,...

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

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G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a $k$ -tuple of orthogonal $n$ -ary operations, where $k < n$ , to an $n$ -tuple of orthogonal $n$ -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a $k$ -tuple of orthogonal $n$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations and an algorithm for complementing a $k$ -tuple of orthogonal $k$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations. Also...

Generalized absolute convergence of single and double Vilenkin-Fourier series and related results

Nayna Govindbhai Kalsariya, Bhikha Lila Ghodadra (2024)

Mathematica Bohemica

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We consider the Vilenkin orthonormal system on a Vilenkin group $G$ and the Vilenkin-Fourier coefficients $\hat{f} (n)$ , $n \in ℕ$ , of functions $f \in L^{p} (G)$ for some $1 < p \leq 2$ . We obtain certain sufficient conditions for the finiteness of the series $\sum_{n = 1}^{\infty} a_{n} {| \hat{f} (n) |}^{r}$ , where ${a_{n}}$ is a given sequence of positive real numbers satisfying a mild assumption and $0 < r < 2$ . We also find analogous conditions for the double Vilenkin-Fourier series. These sufficient conditions are in terms of (either global or local) moduli of continuity of $f$ and give multiplicative...

Computing the greatest $𝐗$ -eigenvector of a matrix in max-min algebra

Ján Plavka (2016)

Kybernetika

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A vector $x$ is said to be an eigenvector of a square max-min matrix $A$ if $A \otimes x = x$ . An eigenvector $x$ of $A$ is called the greatest $𝐗$ -eigenvector of $A$ if $x \in 𝐗 = {x; \underset{̲}{x} \leq x \leq \bar{x}}$ and $y \leq x$ for each eigenvector $y \in 𝐗$ . A max-min matrix $A$ is called strongly $𝐗$ -robust if the orbit $x, A \otimes x, A^{2} \otimes x, \dots$ reaches the greatest $𝐗$ -eigenvector with any starting vector of $𝐗$ . We suggest an $O (n^{3})$ algorithm for computing the greatest $𝐗$ -eigenvector of $A$ and study the strong $𝐗$ -robustness. The necessary and sufficient conditions for strong $𝐗$ -robustness are introduced...

A new algorithm for approximating the least concave majorant

Martin Franců, Ron Kerman, Gord Sinnamon (2017)

Czechoslovak Mathematical Journal

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The least concave majorant, $\hat{F}$ , of a continuous function $F$ on a closed interval, $I$ , is defined by $\hat{F} (x) = inf {G (x) : G \geq F, G concave}, x \in I .$ We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on $I$ . Given any function $F \in 𝒞^{4} (I)$ , it can be well-approximated on $I$ by a clamped cubic spline $S$ . We show that $\hat{S}$ is then a good approximation to $\hat{F}$ . We give two examples, one to illustrate, the other to apply our algorithm. ...

Theoretical analysis for $ℓ_{1}$ - $ℓ_{2}$ minimization with partial support information

Haifeng Li, Leiyan Guo (2025)

Applications of Mathematics

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We investigate the recovery of $k$ -sparse signals using the $ℓ_{1}$ - $ℓ_{2}$ minimization model with prior support set information. The prior support set information, which is believed to contain the indices of nonzero signal elements, significantly enhances the performance of compressive recovery by improving accuracy, efficiency, reducing complexity, expanding applicability, and enhancing robustness. We assume $k$ -sparse signals $𝐱$ with the prior support $T$ which is composed of $g$ true indices and $b$ wrong...

Lanczos-like algorithm for the time-ordered exponential: The $*$ -inverse problem

Pierre-Louis Giscard, Stefano Pozza (2020)

Applications of Mathematics

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The time-ordered exponential of a time-dependent matrix $𝖠 (t)$ is defined as the function of $𝖠 (t)$ that solves the first-order system of coupled linear differential equations with non-constant coefficients encoded in $𝖠 (t)$ . The authors have recently proposed the first Lanczos-like algorithm capable of evaluating this function. This algorithm relies on inverses of time-dependent functions with respect to a non-commutative convolution-like product, denoted by $*$ . Yet, the existence of such inverses,...

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

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This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra $𝔽 S_{n}$ of the symmetric group $S_{n}$ over a field $𝔽$ of characteristic 0 (or $p > n$ ). The goal is to obtain a constructive version of the isomorphism $ψ : ⨁_{λ} M_{d_{λ}} (𝔽) ⟶ 𝔽 S_{n}$ where $λ$ is a partition of $n$ and $d_{λ}$ counts the standard tableaux...

Multifractal analysis of the divergence of Fourier series

Frédéric Bayart, Yanick Heurteaux (2012)

Annales scientifiques de l'École Normale Supérieure

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A famous theorem of Carleson says that, given any function $f \in L^{p} (𝕋)$ , $p \in (1, + \infty)$ , its Fourier series $(S_{n} f (x))$ converges for almost every $x \in 𝕋$ . Beside this property, the series may diverge at some point, without exceeding $O (n^{1 / p})$ . We define the divergence index at $x$ as the infimum of the positive real numbers $β$ such that $S_{n} f (x) = O (n^{β})$ and we are interested in the size of the exceptional sets $E_{β}$ , namely the sets of $x \in 𝕋$ with divergence index equal to $β$ . We show that quasi-all functions in $L^{p} (𝕋)$ have a multifractal behavior with respect to...