Interference in spline-wavelet decompositions

Dem’yanovich, Yu. K.

doi:10.1007/s10958-012-0984-z

Cited by 4 publications

(8 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The proof of formula (4.1) follows the scheme proposed in [2]. Denoting by i s,l the entries of QP T , we illustrate Theorem 3.1 for N = 16, s = 2, r = 6.…”

Section: Lemma 34 the Following Relations Holdmentioning

confidence: 97%

See 1 more Smart Citation

Wavelet decomposition on a comb structure

Dem’yanovich

Dron

2013

J Math Sci

Self Cite

View full text Add to dashboard Cite

We study the interference effect of a two-interval comb structure on a grid. We propose decomposition / reconstruction algorithms and discuss the generation of standing waves. We also obtain estimates for components of the wavelet flow in the case where the original flow is a sequence of the values of a twice continuously differentiable function on a uniform grid. Bibliography: 2 titles. PreliminariesFor any natural number m we denote J m def = {0, 1, . . . , m} and J m def = {−1, 0, 1, . . . , m}. A system of vectors {a i } i∈J m in R 2 is called a complete chain of vectors (cf., for example, [1]) if det(a j−1 , a j ) = 0 for j ∈ J m . Let N be a natural number. On [a, b], we consider a grid

show abstract

“…The proof of formula (4.1) follows the scheme proposed in [2]. Denoting by i s,l the entries of QP T , we illustrate Theorem 3.1 for N = 16, s = 2, r = 6.…”

Section: Lemma 34 the Following Relations Holdmentioning

confidence: 97%

“…We will use the linear space C X introduced by the first author (cf., for example, [2]). We briefly recall how to construct this space.…”

Section: The Embedding Matrixmentioning

confidence: 99%

Wavelet decomposition on a comb structure

Dem’yanovich

Dron

2013

J Math Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…If this condition is satisfied, then in the realization of the algorithm under consideration, with the sth removable node the following wavelet component is associated: (8.15) whereas the removal of node causes certain changes of the structure of the matrices P, Q, U, V. However, a closer location of nodes leads to interference and the corresponding formulas change (cf. [1,2]). …”

Section: Approximation Properties Of Waveletsmentioning

confidence: 99%

“…For this purpose one should use spline approximations of different order, nonuniform girds, and decompositions localized in some parts of the domain, as well as nested decompositions for saving computational resources with taking into account the possibilities of parallel computational systems. These topics were covered in the recent papers [1,2].The goal of this paper is to study the structure of a two-nested spline-wavelet decomposition in the case of distant location of elementary nests. As a result, we obtain algorithms for decomposition / reconstruction and estimate the wavelet flow in the case where the initial flow is a sequence of values of a twice continuously differentiable function on a uniform grid.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Structure of two–nested spline–wavelet decomposition

Dem’yanovich

Dron

2013

J Math Sci

Self Cite

View full text Add to dashboard Cite

We consider the structure of a two-nested first order spline-wavelet decomposition in the case of distant location of elementary nests. We also present algorithms for decomposition and reconstruction and estimate components of the wavelet flow. Bibliography: 2 titles.To study wavelet decompositions of numerical data flows, it is necessary to develop a flexible tool of spline-wavelet approximations with taking into account the smoothness property and the rate of change of the flows. For this purpose one should use spline approximations of different order, nonuniform girds, and decompositions localized in some parts of the domain, as well as nested decompositions for saving computational resources with taking into account the possibilities of parallel computational systems. These topics were covered in the recent papers [1,2].The goal of this paper is to study the structure of a two-nested spline-wavelet decomposition in the case of distant location of elementary nests. As a result, we obtain algorithms for decomposition / reconstruction and estimate the wavelet flow in the case where the initial flow is a sequence of values of a twice continuously differentiable function on a uniform grid.

show abstract