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Chebyshev Approximation of Multivariable Functions by a Power Expression.

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Titel: Chebyshev Approximation of Multivariable Functions by a Power Expression.
Autoren: Malachivskyy, P. S.1 (AUTHOR) Petro.Malachivskyy@gmail.com, Melnychok, L. S.2 (AUTHOR), Pizyur, Ya. V.3 (AUTHOR)
Quelle: Cybernetics & Systems Analysis. Jul2024, Vol. 60 Issue 4, p571-578. 8p.
Schlagwörter: *CHEBYSHEV approximation, *LEAST squares, *ERROR functions, *POLYNOMIALS
Abstract: The paper proposes the method for constructing Chebyshev approximation of multivariable functions with a relative error using a power expression. It involves building an intermediate Chebyshev approximation of values rooted to the corresponding degree of the approximated function by a polynomial with a relative error. Parameters for the polynomial approximation are computed as the boundary mean-power approximation through an iterative scheme using the least squares method with a variable weight function. The authors provide test examples, confirming the fast convergence of the method for constructing the Chebyshev approximation for the functions of one, two, and three variables using power expression. [ABSTRACT FROM AUTHOR]
Datenbank: Academic Search Index
Beschreibung
Abstract:The paper proposes the method for constructing Chebyshev approximation of multivariable functions with a relative error using a power expression. It involves building an intermediate Chebyshev approximation of values rooted to the corresponding degree of the approximated function by a polynomial with a relative error. Parameters for the polynomial approximation are computed as the boundary mean-power approximation through an iterative scheme using the least squares method with a variable weight function. The authors provide test examples, confirming the fast convergence of the method for constructing the Chebyshev approximation for the functions of one, two, and three variables using power expression. [ABSTRACT FROM AUTHOR]
ISSN:10600396
DOI:10.1007/s10559-024-00697-0