Nicolae Crainic (2004)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we characterize the regular UR Birkhoff interpolation schemes ( uniform, rectangular sets of nodes) with rectangular sets of derivatives, and beyond.
Crainic, Nicolae (2003)
Acta Universitatis Apulensis. Mathematics - Informatics
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Crainic, Nicolae (2003)
Acta Universitatis Apulensis. Mathematics - Informatics
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Crainic, Nicolae (2004)
Acta Universitatis Apulensis. Mathematics - Informatics
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Crainic, Nicolae (2003)
Acta Universitatis Apulensis. Mathematics - Informatics
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Jesús Miguel Carnicer, Mariano Gasca (2001)
RACSAM
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La generalización de las fórmulas de interpolación de Lagrange y Newton a varias variables es uno de los temas habituales de estudio en interpolación polinómica. Dos clases de configuraciones geométricas particularmente interesantes en el plano fueron obtenidas por Chung y Yao en 1978 para la fórmula de Lagrange y por Gasca y Maeztu en 1982 para la de Newton. Estos últimos autores conjeturaron que toda configuración de la primera clase es de la segunda, y probaron que el recíproco no...
Phung Van Manh (2015)
Annales Polonici Mathematici
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We give a new poised bivariate Hermite scheme and a formula for the interpolation polynomial. We show that the Hermite interpolation polynomial is the limit of bivariate Lagrange interpolation polynomials at Bos configurations on circles.
Simian, Dana, Simian, Corina (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Rack, Heinz-Joachim, Vajda, Robert (2014)
Serdica Journal of Computing
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ACM Computing Classification System (1998): G.1.1, G.1.2. We consider optimal Lagrange interpolation with polynomials of degree at most two on the unit interval [−1, 1]. In a largely unknown paper, Schurer (1974, Stud. Sci. Math. Hung. 9, 77-79) has analytically described the infinitely many zero-symmetric and zero-asymmetric extremal node systems −1 ≤ x1 < x2 < x3 ≤ 1 which all lead to the minimal Lebesgue constant 1.25 that had already been determined by Bernstein...
Kenta Kobayashi, Takuya Tsuchiya (2016)
Applications of Mathematics
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We consider the error analysis of Lagrange interpolation on triangles and tetrahedrons. For Lagrange interpolation of order one, Babuška and Aziz showed that squeezing a right isosceles triangle perpendicularly does not deteriorate the optimal approximation order. We extend their technique and result to higher-order Lagrange interpolation on both triangles and tetrahedrons. To this end, we make use of difference quotients of functions with two or three variables. Then, the error estimates...
Dovile Karalienė, Zenonas Navickas, Raimondas Čiegis, Minvydas Ragulskis (2015)
Open Mathematics
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An interpolation scheme on an equispaced grid based on the concept of the minimal order of the linear recurrent sequence is proposed in this paper. This interpolation scheme is exact when the number of nodes corresponds to the order of the linear recurrent function. It is shown that it is still possible to construct a nearest mimicking algebraic interpolant if the order of the linear recurrent function does not exist. The proposed interpolation technique can be considered as the extension...