Displaying similar documents to “The general methods of finding the sum S n for all kinds of series”

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

Martin Grigoryan (2010)

Studia Mathematica

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For any 0 < ϵ < 1, p ≥ 1 and each function f L p [ 0 , 1 ] one can find a function g L [ 0 , 1 ) with mesx ∈ [0,1): g ≠ f < ϵ such that its greedy algorithm with respect to the Walsh system converges uniformly on [0,1) and the sequence | c k ( g ) | : k s p e c ( g ) is decreasing, where c k ( g ) is the sequence of Fourier coefficients of g with respect to the Walsh system.

The adaptation of the k -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

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We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is viewed as a Mahalanobis circle with center S , radius r , and some positive definite matrix Σ . A very efficient method for solving this problem is proposed. The method uses a modification of the k -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers...

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,...

An improvement of Euclid's algorithm

Zítko, Jan, Kuřátko, Jan

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The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using c - s transformation and Q R -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.

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,...

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...

On C * -spaces

P. Srivastava, K. K. Azad (1981)

Matematički Vesnik

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A Marchaud type inequality

Jorge Bustamante (2022)

Commentationes Mathematicae Universitatis Carolinae

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We present a new Marchaud type inequality in 𝕃 p spaces.