UDC 519.65
1 Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine
 Petro.Malachivskyy@gmail.com
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2 Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine
levkom@gmail.com
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CHEBYSHEV APPROXIMATION OF MULTIVARIABLE FUNCTIONS
BY THE RATIONAL EXPRESSION WITH THE CONDITION
Abstract. A method for constructing the Chebyshev approximation by the rational expression
of the multivariable functions with the interpolation condition is proposed.
The idea of 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 Lp at p → ∞.
To construct such an approximation, an iterative scheme based on the least squares method
with two variable weight functions is used. One weight function provides the construction
of a mean-power approximation with the interpolation condition, and the second — the specification of the parameters of a rational expression according to the scheme of its linearization. The convergence of the method provides an original way of sequential refinement of the values of weight functions, which takes into account the results of the approximation of previous iterations. The results of test examples confirm the rapid convergence of the proposed method of constructing the Chebyshev approximation by a rational expression with a condition.
Keywords: Chebyshev approximation by the rational expression, Chebyshev approximation with the condition, multivariable functions, mean-power approximation, least squares method, variable weight function.
full text
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