Chebyshev Approximation of the Functions of Many Variables with the Condition

Malachivskyy, P. S.; Melnychok, L. S.; Pizyur, Ya. V.

doi:10.1109/csit49958.2020.9322026

Cited by 7 publications

(4 citation statements)

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“…. of the function f (X) in space E r+2 [18,19], which in accordance with [16,20] coincide to the Chebyshev approximation.…”

Section: The Methods For Determining the Chebyshev Approximation Para...supporting

confidence: 87%

“…The calculation of the parameters of the Chebyshev approximation of multivariable functions with the condition is based on the construction of the boundary mean-power approximation. The least squares method with variable weight function was used for this purpose [18,19]. The possibility of such an approach is investigated in detail in [16].…”

Section: Discussionmentioning

confidence: 99%

“…. [17][18][19]. Suppose that for a function f (X), given by the table on the set of points Ω, there is a Chebyshev approximation of the expression F m (a; X) with the interpolation at subset points U .…”

Section: The Methods For Determining the Chebyshev Approximation Para...mentioning

confidence: 99%

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Chebyshev approximation of multivariable functions with the interpolation

Malachivskyy¹,

Melnychok²,

Pizyur³

2022

Math. Model. Comput.

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A method of constructing a Chebyshev approximation of multivariable functions by a generalized polynomial with the exact reproduction of its values at a given points is proposed. It is based on the sequential construction of mean-power approximations, taking into account the interpolation condition. The mean-power approximation is calculated using an iterative scheme based on the method of least squares with the variable weight function. An algorithm for calculating the Chebyshev approximation parameters with the interpolation condition for absolute and relative error is described. The presented results of solving test examples confirm the rapid convergence of the method when calculating the parameters of the Chebyshev approximation of tabular continuous functions of one, two and three variables with the reproduction of the values of the function at given points.

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“…. of the function f (X) in space E r+2 [18,19], which in accordance with [16,20] coincide to the Chebyshev approximation.…”

Section: The Methods For Determining the Chebyshev Approximation Para...supporting

confidence: 87%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev approximation of multivariable functions with the interpolation

Malachivskyy¹,

Melnychok²,

Pizyur³

2022

Math. Model. Comput.

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“…Ми пропонуємо метод побудови чебишовського наближення функцiй багатьох змiнних рацiональним виразом як граничного наближення у нормi простору L p при p → ∞ [7]. Вiн полягає в послiдовнiй побудовi середньостепеневих наближень з iнтерполяцiйною умовою [10,11]. Значення параметрiв середньостепеневих наближень рацiональним виразом з iнтерполюванням обчислюються з застосуванням iтерацiйної схеми на основi методу найменших квадратiв з використанням двох змiнних вагових функцiй, значення яких уточнюються з врахуванням всiх промiжних середньостепеневих наближень [7,12].…”

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Chebyshev Approximation Multivariable Functions by the Rational Expression With the Interpolation

Malachivskyy¹,

Melnychok²,

Pizyur³

2022

JNAM

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A method for constructing the Chebyshev approximation by the rational expression of the multivariable functions with the interpolation is proposed. The method is based on the construction of the ultimate mean-power approximation by a rational expression with the interpolation condition in the norm of space $L_p$ at $p \to \infty$. To construct such an approximation, an iterative scheme based on the least squares method with two variable weight functions was used.

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