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Article information
2021 , Volume 26, ¹ 2, p.72-87
Shumilov B.M.
On splitting for cubic spline wavelets with four zero moments on an interval
The article examines the problem of constructing a splitting algorithm for cubic spline wavelets. First, a cubic spline space is constructed for splines with homogeneous Dirichlet boundary conditions. Then, using the first four zero moments, the corresponding wavelet space is constructed. The resulting space consists of cubic spline wavelets that satisfy the orthogonality conditions for all thirddegree polynomials. The originality of the research lies in obtaining implicit relations connecting the coefficients of the spline expansion at the initial level with the spline coefficients and wavelet coefficients at the embedded level by a band system of linear algebraic equations with a nondegenerate matrix. Excluding the even rows of the system, the resulting transformation algorithm is obtained as a solution to a sequence of band systems of linear algebraic equations with five (instead of three in the case of two zero moments) diagonals. The presence of strict diagonal dominance over the columns is proved, which confirms the stability of the computational process. For comparison, we adopt the results of calculations using wavelets orthogonal to first-degree polynomials and interpolating cubic spline wavelets with the property of the best mean-square approximation of the second derivative of the function being approximated. The results of numerical experiments show that the scheme with four zero moments is more accurate in the approximation of functions, but becomes inferior in accuracy to the approximation of the second derivative
[full text] [link to elibrary.ru]
Keywords: B-splines, wavelets, implicit decomposition relation
doi: 10.25743/ICT.2021.26.2.006
Author(s):
Shumilov Boris Mihailovich
Dr. , Professor
Position: Professor
Office: Tomsk State University of Architecture and Building
Address: 634003, Russia, Tomsk, Solyanaya square, 2
Phone Office: (382) 2417689
E-mail: sbm@tsuab.ru
SPIN-code: 4445-9076 References:
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Bibliography link:
Shumilov B.M. On splitting for cubic spline wavelets with four zero moments on an interval // Computational technologies. 2021. V. 26. ¹ 2. P. 72-87
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