For the space of (not necessarily polynomial) Hermite type splines we develop algorithms for constructing the spline-wavelet decomposition provided that an arbitrary coarsening of a nonuniform spline-grid is a priori given. The construction is based on approximate relations guaranteeing the asymptotically optimal (with respect to the N-diameter of standard compact sets) approximate properties of this decomposition. We study the structure of restriction and extension matrices and prove that each of these matrices is the one-sided inverse of the transposed other. We propose the decomposition and reconstruction algorithms consisting of a small number of arithmetical actions.
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Dedicated to Nina Nikolaevna Uraltseva
Translated from Problemy Matematicheskogo Analiza98, 2019, pp. 113-126.
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Dem’yanovich, Y.K. Algorithms for Wavelet Decomposition of of the Space of Hermite Type Splines. J Math Sci 242, 133–148 (2019). https://doi.org/10.1007/s10958-019-04470-z
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DOI: https://doi.org/10.1007/s10958-019-04470-z