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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2010, Issue 4, Pages 154–171
(Mi vuu199)
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This article is cited in 5 scientific papers (total in 5 papers)
COMPUTER SCIENCE
Exact formulas for coefficients and residual of optimal approximate spline of simplest heat conduction equation
V. I. Rodionova, N. V. Rodionovab a Faculty of Information Technologies and Computer Engineering, Udmurt State University, Izhevsk, Russia
b Udmurt State University, Izhevsk, Russia
Abstract:
We defined the parameter family of finite-dimensional spaces of special quadratic splines of Lagrange's type. In each space as solution to the initial-boundary problem for the simplest heat conduction equation we propose optimal spline, which gives the smallest residual, which is a norm in the space $\mathrm L_2$. We obtained exact formulas for coefficients of this spline and its residual. The formula for coefficients of this spline is a linear form of finite differences discrete given initial and boundary conditions of the original problem. The formula for the residual is a positive definite quadratic form of these quantities. The coefficients of both forms are computable via Chebyshev's polynomials. We exercised the computer study of the quality of approximation depending on parameters of the family.
Keywords:
interpolation, approximate spline, residual, Chebyshev's polynomials.
Received: 06.04.2010
Citation:
V. I. Rodionov, N. V. Rodionova, “Exact formulas for coefficients and residual of optimal approximate spline of simplest heat conduction equation”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 4, 154–171
Linking options:
https://www.mathnet.ru/eng/vuu199 https://www.mathnet.ru/eng/vuu/y2010/i4/p154
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