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Let sequences {alpha(n)}(n=1)(infinity), {beta(n)}(n=1)(infinity) satisfy the relations alpha(n) is an element of R, beta(n) is an element of R, alpha(n) = o(root n/ln n), beta(n) = o(root n/ln n) as n -> infinity, and let [a, b] subset of (0, pi) and f is an element of C[a, b]. We redefine the function f as F on the interval [0, pi] by polygonal arcs in such a way that the function remains continuous and vanishes on a neighbourhood of the ends of the interval. Also let the function f and the pair of sequences {alpha(n)}(n=1)(infinity), {beta(n)}(n=1)(infinity) be connected by the equiconvergence condition. Then for the classical Lagrange-Jacobi interpolation processes L-n((alpha n,beta n)) (F, cos theta) to approximate f uniformly with respect to theta on [a, b] it is sufficient that f have bounded variation V-a(b) (f) < infinity on [a, b]. In particular, if the sequences {alpha(n)}(n=1)(infinity) and {beta(n)}(n=1)(infinity) are bounded, then for the classical Lagrange-Jacobi interpolation processes L-n((alpha n,beta n)) (F, cos theta) to approximate f uniformly with respect to. on [a, b] it is sufficient that the variation of f be bounded on [a, b], V-a(b) (f) < infinity.

关键词： sinc-approximations interpolation of functions uniform approximation interpolation polynomials bounded variation

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Sufficient Condition for Convergence of Lagrange-Sturm-Liouville Processes in Terms of One-Sided Modulus of Continuity

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2018年第11期58卷 1716-1727页

作者： Trynin, A. Yu. Saratov NG Chernyshevskii State Univ Saratov 410012 Russia

A sufficient condition for the uniform convergence in the interval (0, pi) of interpolation processes based on the eigenfunctions of a regular Sturm-Liouville problem with a continuous bounded variation potential is o... 详细信息

关键词： sinc approximation interpolation of functions uniform approximation Lagrange-Sturm-Liouville processes

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Application of a Continuant to the Estimation of a Remainder Term of Thiele’s interpolation Continued Fraction

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Journal of Mathematical Sciences (United States) 2020年第5期246卷 687-700页

作者： Pahirya, Mykhaylo M. Uzhhorod National University Mukachevo State University Mukachevo Ukraine

New properties of a continuant has been proved. Using the relationship between the continuant and the continued fraction, an estimate of the remainder term of Thiele’s interpolation continued fraction is obtained. &#... 详细信息

关键词： continuant Continued fraction interpolation of functions remainder term

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Taylorian fields and subdivision algorithms

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Numerical Algorithms 1991年第2期1卷 225-235页

作者： Le Méhauté, A. Laboratoire d'Analyse Numérique et d'Optimisation Université de Lille 1 Flandres-Artois Villeneuve d'Ascq Cedex 59655 France

Some recents papers [3,8] provide a new approach for the concept of subdivision algorithms, widely used in CAGD: they develop the idea of interpolatory subdivision schemes for curves. In this paper, we show how the old results of H. Whitney [13,14] on Taylorian fields giving necessary and sufficient conditions for a function to be of class C^k on a compact provide also necessary and sufficient conditions which can be used to construct interpolatory subdivision schemes, in order to obtain, at the limit, a C¹ (or C^k, k>1 eventually) function. Moreover, we give general results for the approximation properties of these schemes, and error bounds for the approximation of a given function. © 1991 J.C. Baltzer A.G. Scientific Publishing Company.

关键词： CAGD extension theorems interpolation of functions shape preservation subdivision algorithms Subject Classifications: AMS (Mos), 65D05 Taylorian fields

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A Criterion of Convergence of Lagrange-Sturm-Liouville Processes in Terms of One-Sided Module of Variation

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RUSSIAN MATHEMATICS 2018年第8期62卷 51-63页

作者： Trynin, A. Yu. Saratov NG Chernyshevskii State Univ Ul Astrakhanskaya 83 Saratov 410012 Russia

We obtain a criterion of uniform convergence inside the interval (0, pi) of interpolation processes determined by eigenfunctions of the regular Sturm-Liouville problem with a continuous potential of bounded variation.... 详细信息

关键词： sinc approximation interpolation of functions uniform approximation Lagrange-Sturm-Liouville processes

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Approximation of Continuous on a Segment functions With the Help of Linear Combinations of Sincs

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RUSSIAN MATHEMATICS 2016年第3期60卷 63-71页

作者： Trynin, A. Yu. Saratov NG Chernyshevskii State Univ Ul Astrakhanskaya 33 Saratov 410012 Russia

We investigate approximative properties of various operators, that are modifications of sinc-approximations of continuous functions on a segment.

关键词： sinc-approximation interpolation of functions uniform approximation

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