2010/04/19 by Costanza Conti, Conti, Costanza, Luca Gemignani +3
Engineering · #65D05 #65F05 #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Tribology and Lubrication Engineering
paper · pdf · doi:10.48550/arxiv.1004.3232
openalex publication_date 2010/04/19 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
In this paper we describe a general, computationally feasible strategy to\ndeduce a family of interpolatory non-stationary subdivision schemes from a\nsymmetric non-stationary, non-interpolatory one satisfying quite mild\nassumptions. To achieve this result we extend our previous work [C.Conti,\nL.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] to\nfull generality by removing additional assumptions on the input symbols. For\nthe so obtained interpolatory schemes we prove that they are capable of\nreproducing the same exponential polynomial space as the one generated by the\noriginal approximating scheme. Moreover, we specialize the computational\nmethods for the case of symbols obtained by shifted non-stationary affine\ncombinations of exponential B-splines, that are at the basis of most\nnon-stationary subdivision schemes. In this case we find that the associated\nfamily of interpolatory symbols can be determined to satisfy a suitable set of\ngeneralized interpolating conditions at the set of the zeros (with reversed\nsigns) of the input symbol. Finally, we discuss some computational examples by\nshowing that the proposed approach can yield novel smooth non-stationary\ninterpolatory subdivision schemes possessing very interesting reproduction\nproperties.\n