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

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Abstract

In this paper we describe a general, computationally feasible strategy to deduce a family of interpolatory non-stationary subdivision schemes from a symmetric non-stationary, non-interpolatory one satisfying quite mild assumptions. To achieve this result we extend our previous work (Conti et al., Linear Algebra Appl 431(10):1971–1987, 2009) to full generality by removing additional assumptions on the input symbols. For the so obtained interpolatory schemes we prove that they are capable of reproducing the same space of exponential polynomials as the one generated by the original approximating scheme. Moreover, we specialize the computational methods for the case of symbols obtained by shifted non-stationary affine combinations of exponential B-splines, that are at the basis of most non-stationary subdivision schemes. In this case we find that the associated family of interpolatory symbols can be determined to satisfy a suitable set of generalized interpolating conditions at the set of the zeros (with reversed signs) of the input symbol. Finally, we discuss some computational examples by showing that the proposed approach can yield novel smooth non-stationary interpolatory subdivision schemes possessing very interesting reproduction properties.

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Authors and Affiliations

  1. Dipartimento di Energetica “Sergio Stecco”, Università di Firenze, Via Lombroso 6/17, 50134, Firenze, Italy

    Costanza Conti

  2. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Luca Gemignani

  3. Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via R. Cozzi 53, 20125, Milano, Italy

    Lucia Romani

Authors
  1. Costanza Conti
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  2. Luca Gemignani
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  3. Lucia Romani
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Correspondence to Costanza Conti.

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Communicated by Juan Manuel Peña.

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Conti, C., Gemignani, L. & Romani, L. From approximating to interpolatory non-stationary subdivision schemes with the same generation properties. Adv Comput Math 35, 217–241 (2011). https://doi.org/10.1007/s10444-011-9175-6

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  • DOI: https://doi.org/10.1007/s10444-011-9175-6

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