Nonlinear approximation of functions based on nonnegative least squares solver

In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required parameters. The approximating function is linear in the first param...

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Главные авторы:	Vabishchevich, P. N., Вабищевич, П. Н.
Формат:	Статья
Язык:	English
Опубликовано:	2023
Темы:	Approximation by the sum of exponents Rational approximation Nonnegative least squares method Nonlinear approximation of function
Online-ссылка:	https://dspace.ncfu.ru/handle/20.500.12258/25188
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spelling	ir-20.500.12258-251882025-02-12T09:46:01Z Nonlinear approximation of functions based on nonnegative least squares solver Vabishchevich, P. N. Вабищевич, П. Н. Approximation by the sum of exponents Rational approximation Nonnegative least squares method Nonlinear approximation of function In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required parameters. The approximating function is linear in the first parameter; these parameters are assumed to be positive. The individual terms of the approximating function represent a fixed function that depends nonlinearly on the second parameter. A numerical approximation minimizes the residual functional by approximating function values at individual points. The second parameter's value is set on a more extensive set of points of the interval of permissible values. The proposed approach's key feature consists in determining the first parameter on each separate iteration of the classical nonnegative least squares method. The computational algorithm is used to rational approximate the function (Formula presented.). The second example concerns the approximation of the stretching exponential function (Formula presented.) at (Formula presented.) by the sum of exponents. 2023-09-07T07:49:25Z 2023-09-07T07:49:25Z 2023 Статья Vabishchevich, P.N. Nonlinear approximation of functions based on nonnegative least squares solver // Numerical Linear Algebra with Applications. - 2023. - 30 (6). - статья № e2522. - DOI: 10.1002/nla.2522 http://hdl.handle.net/20.500.12258/25188 en Numerical Linear Algebra with Applications application/pdf application/pdf
institution	СКФУ
collection	Репозиторий
language	English
topic	Approximation by the sum of exponents Rational approximation Nonnegative least squares method Nonlinear approximation of function
spellingShingle	Approximation by the sum of exponents Rational approximation Nonnegative least squares method Nonlinear approximation of function Vabishchevich, P. N. Вабищевич, П. Н. Nonlinear approximation of functions based on nonnegative least squares solver
description	In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required parameters. The approximating function is linear in the first parameter; these parameters are assumed to be positive. The individual terms of the approximating function represent a fixed function that depends nonlinearly on the second parameter. A numerical approximation minimizes the residual functional by approximating function values at individual points. The second parameter's value is set on a more extensive set of points of the interval of permissible values. The proposed approach's key feature consists in determining the first parameter on each separate iteration of the classical nonnegative least squares method. The computational algorithm is used to rational approximate the function (Formula presented.). The second example concerns the approximation of the stretching exponential function (Formula presented.) at (Formula presented.) by the sum of exponents.
format	Статья
author	Vabishchevich, P. N. Вабищевич, П. Н.
author_facet	Vabishchevich, P. N. Вабищевич, П. Н.
author_sort	Vabishchevich, P. N.
title	Nonlinear approximation of functions based on nonnegative least squares solver
title_short	Nonlinear approximation of functions based on nonnegative least squares solver
title_full	Nonlinear approximation of functions based on nonnegative least squares solver
title_fullStr	Nonlinear approximation of functions based on nonnegative least squares solver
title_full_unstemmed	Nonlinear approximation of functions based on nonnegative least squares solver
title_sort	nonlinear approximation of functions based on nonnegative least squares solver
publishDate	2023
url	https://dspace.ncfu.ru/handle/20.500.12258/25188
work_keys_str_mv	AT vabishchevichpn nonlinearapproximationoffunctionsbasedonnonnegativeleastsquaressolver AT vabiŝevičpn nonlinearapproximationoffunctionsbasedonnonnegativeleastsquaressolver
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Nonlinear approximation of functions based on nonnegative least squares solver

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