Displaying similar documents to “An adaptive s -step conjugate gradient algorithm with dynamic basis updating”

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,...

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.

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...

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...

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.

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...

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 ⊗ x = x . An eigenvector x of A is called the greatest 𝐗 -eigenvector of A if x ∈ 𝐗 = { x ; x ̲ ≤ x ≤ x ¯ } and y ≤ x for each eigenvector y ∈ 𝐗 . A max-min matrix A is called strongly 𝐗 -robust if the orbit x , A ⊗ x , A 2 ⊗ x , ⋯ 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...