Dubuc--Deslauriers Subdivision for Finite Sequences and Interpolation Wavelets on an Interval

Villiers, J. M. De; Goosen, K. M.; Herbst, B. M.

doi:10.1137/s0036141001386830

Cited by 18 publications

(19 citation statements)

References 18 publications

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“…The derivation in this section is based on the work done by de Villiers, Goosen and Herbst [22] and [19]. We denote by P 2n+1 the space of all polynomials of degree ≤ 2n + 1 for a nonnegative integer n. In our argument, the Lagrange fundamental polynomials {L k (x)} n+1 k=−n corresponding to the nodes {k} n+1 k=−n play quite an important role.…”

Section: Construction Of the Polynomial Reproducing Maskmentioning

confidence: 99%

“…And we take the value of the parameter v as v = 0, the proposed scheme becomes the (2n + 4)-point interpolatory symmetric subdivision scheme, and when v = w = 0, it becomes the well-known (2n + 2)-DD scheme [22] of which the mask, denoted by {a…”

Section: Construction Of the Polynomial Reproducing Maskmentioning

confidence: 99%

“…Then the mask {b i } i∈Z satisfies the polynomial reproduction property of degree L, Proof. Assume that the mask {b i } i∈Z satisfies the polynomial reproduction property (22). Substituting p(x) = 1 into (22), we obtain the identities (23).…”

Section: Construction Of the Polynomial Reproducing Maskmentioning

confidence: 99%

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Construction of a Symmetric Subdivision Scheme Reproducing Polynomials

Ko¹

2016

Communications of the Korean Mathematical Society

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Abstract. In this work, we study on subdivision schemes reproducing polynomials and build a symmetric subdivision scheme reproducing polynomials of a certain predetermined degree, which is a slight variant of the family of Deslauries-Dubic interpolatory ones. Related to polynomial reproduction, a necessary and sufficient condition for a subdivision scheme to reproduce polynomials of degree L was recently established under the assumption of non-singularity of subdivision schemes. In case of stepwise polynomial reproduction, we give a characterization for a subdivision scheme to reproduce stepwise all polynomials of degree ≤ L without the assumption of non-singularity. This characterization shows that we can investigate the polynomial reproduction property only by checking the odd and even masks of the subdivision scheme.The minimal-support condition being relaxed, we present explicitly a general formula for the mask of (2n + 4)-point symmetric subdivision scheme with two parameters that reproduces all polynomials of degree ≤ 2n+1. The uniqueness of such a symmetric subdivision scheme is proved, provided the two parameters are given arbitrarily. By varying the values of the parameters, this scheme is shown to become various other well known subdivision schemes, ranging from interpolatory to approximating.

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Section: Construction Of the Polynomial Reproducing Maskmentioning

confidence: 99%

Section: Construction Of the Polynomial Reproducing Maskmentioning

confidence: 99%

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Construction of a Symmetric Subdivision Scheme Reproducing Polynomials

Ko¹

2016

Communications of the Korean Mathematical Society

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“…A particularly important example is the 2n-point interpolatory Dubuc-Deslauriers scheme, where n ∈ N is fixed. It is shown in [3] that the mask can be constructed as the sequence of minimal support satisfying a certain polynomial filling property, and this gives rise to the explicit formula…”

Section: Introductionmentioning

confidence: 99%

“…Applying the duplication formula Γ(x)Γ(x + where r 0 and s 0 are the largest integers less than or equal to r and s respectively derived in [3] and used in [2]. However, we will make use of Stirling's approximation…”

Section: Introductionmentioning

confidence: 99%

A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc–Deslauriers subdivision scheme

Bez¹,

Bez²

2014

LMS J. Comput. Math.

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We analyse the mask associated with the 2n-point interpolatory Dubuc-Deslauriers subdivision scheme S a [n] . Sharp bounds are presented for the magnitude of the coefficients a2i−1 | is comparable to i −1 , and for larger power scales, exponentially decaying bounds are obtained. Using our bounds, we may precisely analyse the summability of the mask as a function of n by identifying which coefficients of the mask contribute to the essential behaviour in n, recovering and refining the recent result of DengHormann-Zhang that the operator norm of S a [n] on ∞ grows logarithmically in n.

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On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions

Rabarison

Villiers

2010

Approximation Algorithms for Complex Systems

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Dubuc--Deslauriers Subdivision for Finite Sequences and Interpolation Wavelets on an Interval

Cited by 18 publications

References 18 publications

Construction of a Symmetric Subdivision Scheme Reproducing Polynomials

Construction of a Symmetric Subdivision Scheme Reproducing Polynomials

A note on magnitude bounds for the mask coefficients of the interpolatory Dubuc–Deslauriers subdivision scheme

On Bivariate Interpolatory Mask Symbols, Subdivision and Refinable Functions

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