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In this paper we describe a general, computationally feasible strategy todeduce a family of interpolatory non-stationary subdivision schemes from asymmetric non-stationary, non-interpolatory one satisfying quite mildassumptions. To achieve this result we extend our previous work [C.Conti,L.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] tofull generality by removing additional assumptions on the input symbols. Forthe so obtained interpolatory schemes we prove that they are capable ofreproducing the same exponential polynomial space as the one generated by theoriginal approximating scheme. Moreover, we specialize the computationalmethods for the case of symbols obtained by shifted non-stationary affinecombinations of exponential B-splines, that are at the basis of mostnon-stationary subdivision schemes. In this case we find that the associatedfamily of interpolatory symbols can be determined to satisfy a suitable set ofgeneralized interpolating conditions at the set of the zeros (with reversedsigns) of the input symbol. Finally, we discuss some computational examples byshowing that the proposed approach can yield novel smooth non-stationaryinterpolatory subdivision schemes possessing very interesting reproductionproperties.

From approximating to interpolatory non-stationary subdivision schemes with the same generation properties