On Trigonometric Blending Interpolation and Cubature Formulae |
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Authors: | Dimiter Dryanov Petar Petrov |
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Institution: | 1. Concordia University, Montreal, QC, H3G 1M8, Canada 2. Leibniz Institute for Crystal Growth, Max-Born-Str. 2, 12489, Berlin, Germany 3. Faculty of Mathematics and Informatics, Sofia University, James Bourchier blvd. 5, 1164, Sofia, Bulgaria
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Abstract: | We discuss error representations for Hermite-Lagrange trigonometric interpolation introduced in Dryanov and Petrov (Interpolation and L 1-approximation by trigonometric polynomials and blending functions, J. Approx. Theory 164, 1049–1064 (2012)) and obtain one-sided trigonometric quadratures for approximate integration of one-dimensional integrals. Next, we study error representations of multivariate Hermite-Lagrange transfinite trigonometric interpolation and derive one-sided trigonometric blending interpolants to multivariate functions, under some restrictions. Then, we construct one-sided transfinite cubature formulae for approximate integration of multivariate integrals. We construct also cubature formulae with positive coefficients, based on line integrals and exact in a vector space of trigonometric blending functions with prescribed order. |
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