Abstract
We examine Faber’s type decompositions for spaces of linear minimal splines constructed on nonuniform grids on a segment. A characteristic feature of the Faber decomposition is that the basis wavelets are centered around the knots that do not belong to the coarse grid. The construction of the lazy wavelets begins with the use of the basis functions in refined spline space centered at the odd knots. We propose to use as wavelets the functions centered at the even knots under some conditions. In contrast to lazy wavelets, in this case the decomposition system of equations has a unique solution, which can be found by the sweep method with the guarantee of well-posedness and stability.
The reported study was funded by a grant of the President of the Russian Federation (MD-2242.2019.9).
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Makarova, S., Makarov, A. (2020). On Linear Spline Wavelets with Shifted Supports. In: Sergeyev, Y., Kvasov, D. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2019. Lecture Notes in Computer Science(), vol 11974. Springer, Cham. https://doi.org/10.1007/978-3-030-40616-5_40
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DOI: https://doi.org/10.1007/978-3-030-40616-5_40
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