A family of non-oscillatory 6-point interpolatory subdivision schemes
View/ Open
Impact
Scholar |
Other documents of the author: Donat Beneito, Rosa María; López-Ureña, Sergio; Santágueda-Villanueva, María
Metadata
Show full item recordcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/8017
comunitat-uji-handle3:10234/8616
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
A family of non-oscillatory 6-point interpolatory subdivision schemesDate
2017-02Publisher
Springer VerlagBibliographic citation
DONAT, Rosa; LÓPEZ-UREÑA, Sergio; SANTÁGUEDA, Maria. A family of non-oscillatory 6-point interpolatory subdivision schemes. Advances in Computational Mathematics, p. 1-35.Type
info:eu-repo/semantics/articlePublisher version
http://link.springer.com/article/10.1007/s10444-016-9509-5Subject
Abstract
In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered non-oscillatory versions of the 6-point Deslauries-Dubuc (DD) interpolatory scheme, just as the Power p schemes ... [+]
In this paper we propose and analyze a new family of nonlinear subdivision schemes which can be considered non-oscillatory versions of the 6-point Deslauries-Dubuc (DD) interpolatory scheme, just as the Power p schemes are considered nonlinear non-oscillatory versions of the 4-point DD interpolatory scheme. Their design principle may be related to that of the Power p schemes and it is based on a weighted analog of the Power p mean. We prove that the new schemes reproduce exactly polynomials of degree three and stay ’close’ to the 6-point DD scheme in smooth regions. In addition, we prove that the first and second difference schemes are well defined for each member of the family, which allows us to give a simple proof of the uniform convergence of these schemes and also to study their stability as in [19, 22]. However our theoretical study of stability is not conclusive and we perform a series of numerical experiments that seem to point out that only a few members of the new family of schemes are stable. On the other hand, extensive numerical testing reveals that, for smooth data, the approximation order and the regularity of the limit function may be similar to that of the 6-point DD scheme and larger than what is obtained with the Power p schemes. [-]
Is part of
Adv Comput Math (2017)Rights
© Springer Science+Business Media New York 2017
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- EDU_Articles [504]