A new family of non-stationary hermite subdivision schemes reproducing exponential polynomials

Byeongseon Jeong, Jungho Yoon

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Abstract

In this study, we present a new class of quasi-interpolatory non-stationary Hermite subdivision schemes reproducing exponential polynomials. This class extends and unifies the well-known Hermite schemes, including the interpolatory schemes. Each scheme in this family has tension parameters which provide design flexibility, while obtaining at least the same or better smoothness compared to an interpolatory scheme of the same order. We investigate the convergence and smoothness of the new schemes by exploiting the factorization tools of non-stationary subdivision operators. Moreover, a rigorous analysis for the approximation order of the non-stationary Hermite scheme is presented. Finally, some numerical results are presented to demonstrate the performance of the proposed schemes. We find that the quasi-interpolatory scheme can circumvent the undesirable artifacts appearing in interpolatory schemes with irregularly distributed control points.

Original languageEnglish
Article number124763
JournalApplied Mathematics and Computation
Volume366
DOIs
StatePublished - 1 Feb 2020

Bibliographical note

Funding Information:
Byeongseon Jeong was supported by the grant NRF-2019R1I1A1A01060757 and NRF-2019R1A6A1A11051177 funded by the Ministry of Education. Jungho Yoon was supported by the grant NRF-2015R1A5A1009350 and NRF-2019R1F1A1060804 through the NRF ( National Research Foundation ).

Publisher Copyright:
© 2019 Elsevier Inc.

Keywords

  • Approximation order
  • Convergence
  • Exponential polynomial reproduction
  • Non-stationary hermite subdivision scheme
  • Smoothness

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