Results 251 to 260 of about 547,161 (285)

Approximation ratio of the digits in Oppenheim series expansion

Publicationes Mathematicae Debrecen, 2008
Summary: This paper is concerned with the Hausdorff dimensions of some sets determined by the approximation ratio of the digits in Oppenheim series expansion. We give a general characterization on the Hausdorff dimensions of such sets. As its corollaries, we answer questions posed by J. Galambos.
Wang, Baowei, Wu, Jun
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Series expansions and approximations

2002
Chapter 12 dealt with infinite series of numbers and criteria for their convergence. In the same way one can study infinite series of functions $$\sum\limits_{k = 0}^\infty {{u_k}\left( x \right)} $$ where the functions uk (x) are all defined on a common interval.
Adi Ben-Israel, Robert Gilbert
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Fast Kernel Matrix Approximations By Series Expansions

2022
169 pages ; Kernel functions are used in a variety of scientific settings to measure relationships or interactions between elements of a vector space. For example, in machine learning, kernel functions are often used to describe similarity or covariance between data points in a feature space.
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Inhomogeneous and simultaneous Diophantine approximation in Cantor series expansions

Journal of Mathematical Analysis and Applications
This paper is concerned with inhomogeneous and simultaneous Diophantine approximation for the nonautonomous dynamical system induced by Cantor series expansion. Let \(Q =\{q_k\}_{k\ge 1}\) be a sequence of positive integers with \(q_k\ge 2\) for all \(k\ge 1\). For any positive integer \(n\), the transformations \(T_{Q,n}:[0,1)\to[0,1)\) and \(T_{Q}^{n}
Baiyang Zhang
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Approximate structural reanalysis based on series expansion

Computer Methods in Applied Mechanics and Engineering, 1981
Abstract In most optimal design procedures the analysis of the structure must be repeated many times. This operation, which involves much computational effort, is one of the main difficulties in applying optimization methods to large systems. This study deals with approximate reanalysis methods based on series expansion.
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An approximate Wiener-series expansion and a condition of stationarity for some quadratic time series models

Publicationes Mathematicae Debrecen, 2022
Wiener-Itô integrals are used to give the Wiener series expansion for a quadratic of the observation model which is a special case of the state dependent model. Wiener kernels for the product of two nonlinear processes are determined. Some explicit formulae for the product of multiple Wiener-Itô integrals are received.
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On the Estimate of the K-Factor: An Effective Approximation Based on Taylor Series Expansion

IEEE Transactions on Electromagnetic Compatibility, 2020
In this letter, an approximate estimator of the K -factor ( K ) for wireless channels is obtained. It is based on the use of a second-order Taylor expansion of the analytical expression of the K maximum likelihood estimator (MLE) of available in the literature for wireless channels emulated in reverberation chamber.
Gifuni, Angelo, Perna, Stefano
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A recursive method for the approximate expansion of functions in a series of polynomials

Computer Physics Communications, 1972
Abstract In this paper we describe a recursive procedure for the approximate evaluation of the coefficients of expansion of a function y(x) in a system of polynomials λ = [λk(x)], k∈N. Numerical examples and the computational procedure are also discussed.
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A Comparison of “Best” Polynomial Approximations with Truncated Chebyshev Series Expansions

Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis, 1964
Introduction. In the numerical solution of mathematical problems it is common to represent a function of a real variable by the leading terms of its infinite Chebyshev series expansion. The purpose of this paper is to compare the accuracy of such a polynomial approximation with that of the "best" polynomial approximation of the same degree (the "best ...
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Linear Approximations of Nonlinear Relationships by the Taylor's Series Expansion Revisited

1972
This paper examines the magnitude of error associated with linear approximations of nonlinear variables based on Taylor's Series. Little attention has been given to the error term in previous empirical studies. This paper presents the mathematical technique for the single-variable and twovariable cases.
Womack, Abner W., Matthews, Jimmy L.
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