2019/07/22 by Lucia Romani, Romani, Lucia, Alberto Viscardi +1
Engineering · #Advanced Numerical Analysis Techniques #Advanced Surface Polishing Techniques #Advanced machining processes and optimization #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1907.09185
openalex publication_date 2019/07/22 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
A new class of univariate stationary interpolatory subdivision schemes of\ndual type is presented. As opposed to classical primal interpolatory schemes,\nthese new schemes have masks with an even number of elements and are not\nstep-wise interpolants. A complete algebraic characterization, which covers\nevery arity, is given in terms of identities of trigonometric polynomials\nassociated to the schemes. This characterization is based on a necessary\ncondition for refinable functions to have prescribed values at the nodes of a\nuniform lattice, as a consequence of the Poisson summation formula. A strategy\nfor the construction is then showed, alongside meaningful examples for\napplications that have comparable or even superior properties, in terms of\nregularity, length of the support and/or polynomial reproduction, with respect\nto the primal counterparts.\n