Results 21 to 30 of about 302,091 (291)
ON THE CONVERGENCE OF THE LEAST SQUARE METHOD IN CASE OF NON-UNIFORM GRIDS
Проблемы анализа, 2019 Let f(t) be a continuous on [−1, 1] function, which values are given at the points of arbitrary non-uniform grid ΩN = = {tj} N−1 j=0 , where nodes tj satisfy the only condition ηj 6tj 6ηj+1, 0 6 j 6 N − 1, and nodes ηj are such that −1 = η0 < η1 < η2
M. S. Sultanakhmedov
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Наука. Инновации. Технологии, 2022 Introduction: the methods of representation of functions given approximately by their singular integrals in relation to approximation problems and numerical methods for solving boundary value problems for differential equations are Investigated.
Igor Eduardovich Naats +2 more
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A Deep-Network Piecewise Linear Approximation Formula
IEEE Access, 2021 The mathematical foundation of deep learning is the theorem that any continuous function can be approximated within any specified accuracy by using a neural network with certain non-linear activation functions. However, this theorem does not tell us what
Gengsheng L. Zeng
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Taylor Polynomials in a High Arithmetic Precision as Universal Approximators
ComputationFunction approximation is a fundamental process in a variety of problems in computational mechanics, structural engineering, as well as other domains that require the precise approximation of a phenomenon with an analytic function. This work demonstrates
Nikolaos Bakas
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Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 2023 Artificial neural networks are essential intelligent tools for various learning tasks. Training them is challenging due to the nature of the data set, many training weights, and their dependency, which gives rise to a complicated high-dimensional error ...
Saithip Limtrakul +1 more
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The Principle of Localization at the Class of Functions Integrable in the Riemann for the Processes of Lagrange - Sturm - Liouville [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 Let us say that the principle of localization holds at the class of functions $F$ at point $x_0 \in [0, \pi]$ for the Lagrange\,--\,Sturm\,--\,Liouville interpolation process $L_n^{SL}(f,x)$ if $\lim_{n \rightarrow \infty}\left|L_n^{SL}(f, x_0)-L_n^{SL ...
Aleksandr Yurievich Trynin +1 more
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Dual Taylor Series, Spline Based Function and Integral Approximation and Applications
Mathematical and Computational Applications, 2019 In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series ...
Roy M. Howard
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Pediatric Blood &Cancer, EarlyView.ABSTRACT The pediatric hematology‐oncology fellowship training curriculum has not substantially changed since its inception. The first year of training is clinically focused, and the second and third years are devoted to scholarship. However, this current structure leaves many fellows less competitive in the current job market, resulting in ...
Scott C. Borinstein +3 more
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Random vector functional link networks for function approximation on manifolds
Frontiers in Applied Mathematics and StatisticsThe learning speed of feed-forward neural networks is notoriously slow and has presented a bottleneck in deep learning applications for several decades. For instance, gradient-based learning algorithms, which are used extensively to train neural networks,
Deanna Needell +4 more
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Наука. Инновации. Технологии, 2022 Introduction: the presented work continues the authors' research on the methods of the theory of approximation of functions of a real variable, given approximately, on the basis of their representation by integrals. Materials and methods of research: the
Igor Naats +2 more
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