Minimization of Errors of the Polynomial- Trigonometric Interpolation with Shifted Nodes∗
نویسندگان
چکیده
The polynomial-trigonometric interpolation based on the Krylov approach for a smooth function given on [-1, 1] is defined on the union of m shifted each other uniform grids with the equal number of points. The asymptotic errors of the interpolation in both uniform and L2 metrics are investigated. It turned out that the corresponding errors can be minimized due to an optimal choice of the shift parameters. The study of asymptotic errors is based on the concept of the ”limit function” proposed by Vallee-Poussin. In particular cases of unions of two and three uniform grids the limit functions are found explicitly and the optimal shift parameters are calculated using MATHEMATICA 4.1 computer system. The parallel processing is investigated.
منابع مشابه
On a pointwise convergence of trigonometric interpolations with shifted nodes
We consider trigonometric interpolations with shifted equidistant nodes and investigate their accuracies depending on the shift parameter. Two different types of interpolations are in the focus of our attention: the Krylov-Lanczos and the rational-trigonometric-polynomial interpolations. In both cases, we find optimal shifts that provide with the best accuracy in different frameworks.
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