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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2010, Issue 2, Pages 127–132
(Mi vuu159)
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This article is cited in 1 scientific paper (total in 1 paper)
COMPUTER SCIENCE
On family of interpolated polynomials of some variables
V. I. Rodionov Udmurt State University
Abstract:
The one-parametrical family of quadratic interpolated polynomials of several variables is investigated. In a role of parameter the point of $n$-dimensional space acts. Questions of existence and uniqueness interpolated polynomials are investigated. For polynomials the obvious representation (in barycentric system of coordinates) is proved. It is shown that only for the unique parameter continuous docking of interpolated polynomials constructed on elements of a triangulation of a special type takes place. For interpolated polynomial appropriating the given parameter the obvious representation in the Cartesian system of coordinates is proved. Application of interpolation with the given parameter makes possible quadratic spline-approximation of functions of many variables (at the same time with approximation of a field of a gradient of this function).
Keywords:
interpolation, approximation, multivariate spline, gradient, simplex, barycentric coordinate system.
Received: 15.02.2010
Citation:
V. I. Rodionov, “On family of interpolated polynomials of some variables”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 2, 127–132
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https://www.mathnet.ru/eng/vuu159 https://www.mathnet.ru/eng/vuu/y2010/i2/p127
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Abstract page: | 281 | Full-text PDF : | 202 | References: | 44 | First page: | 1 |
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