Cubic spline wavelets with complementary boundary conditions

Černá, Dana; Finěk, Václav

doi:10.1016/j.amc.2012.08.027

Cited by 11 publications

(3 citation statements)

References 22 publications

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“…Proposition 1 For L = 3 equation ( 11) is verified by direct calculation using the example (7) and definitions…”

Section: Corollarymentioning

confidence: 90%

“…Indeed, from the speed of approximation of smooth functions [5, p. 52, 156] these two types of wavelets are equivalent, and orthogonality to polynomials provides a locally maximal "likeness" to a better rootmean-square approach. At the same time in statistical applications, orthogonality for polynomials of high degree is not required at all [6], in contrast, for example, to the problem of numerical differentiation [7].…”

Section: Introductionmentioning

confidence: 99%

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Shifted Cubic Spline Wavelets with Two Vanishing Moments on the Interval and a Splitting Algorithm

Shumilov

2020

Wseas Transactions on Systems

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This paper deals with the use of the first two vanishing moments for constructing cubic spline-wavelets orthogonal to polynomials of the first degree. A decrease in the supports of these wavelets is shown in comparison with the classical semiorthogonal wavelets. For splines with homogeneous Dirichlet boundary conditions of the second order, an algorithm of the shifted wavelet transform is obtained in the form of a solution of a tridiagonal system of linear equations with a strict diagonal dominance

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“…Proposition 1 For L = 3 equation ( 11) is verified by direct calculation using the example (7) and definitions…”

Section: Corollarymentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Shifted Cubic Spline Wavelets with Two Vanishing Moments on the Interval and a Splitting Algorithm

Shumilov

2020

Wseas Transactions on Systems

View full text Add to dashboard Buy / Rent full text

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“…Spline wavelet or multiwavelet bases where duals are not local are also known. 6,13,15,14,16 The advantage of our construction in comparison with biorthogonal cubic spline wavelets with local duals 2,3,12,18 is that the support of the wavelets is shorter, condition numbers of the corresponding stiffness matrices are smaller and also a simple construction.…”

Section: Dčerná and V Finěkmentioning

confidence: 99%

Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions

Černá

Finěk

2015

Int. J. Wavelets Multiresolut Inf. Process.

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In this paper, we propose a construction of a new cubic spline-wavelet basis on the hypercube satisfying homogeneous Dirichlet boundary conditions. Wavelets have two vanishing moments. Stiffness matrices arising from discretization of elliptic problems using a constructed wavelet basis have uniformly bounded condition numbers and we show that these condition numbers are small. We present quantitative properties of the constructed basis and we provide a numerical example to show the efficiency of the Galerkin method using the constructed basis.

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Cubic spline wavelets with complementary boundary conditions

Cited by 11 publications

References 22 publications

Shifted Cubic Spline Wavelets with Two Vanishing Moments on the Interval and a Splitting Algorithm

Shifted Cubic Spline Wavelets with Two Vanishing Moments on the Interval and a Splitting Algorithm

Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions

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