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Wavelet bases of Hermite cubic splines on the interval

Rong-Qing Jia, Song-Tao Liu
2006 Advances in Computational Mathematics  
In this paper a pair of wavelets are constructed on the basis of Hermite cubic splines. These wavelets are in C 1 and supported on [−1, 1].  ...  The computational results demonstrate the advantage of the wavelet basis. Keywords: wavelets on the interval, Hermite cubic splines, numerical solutions of differential equations.  ...  Liu / Wavelet bases of Hermite cubic splines  ... 
doi:10.1007/s10444-003-7609-5 fatcat:342hkgk57jdhtkhljvlrzej4ry

Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines

K. Maleknejad, M. Yousefi
2006 Applied Mathematics and Computation  
Introduction Here we shall construct wavelet basis of Hermite cubic splines on the interval. These wavelet basis are suitable for numerical solutions of integral equations.  ...  Smooth orthogonal wavelets with compact support were constructed by Daubechies [4}. The Daubechies orthogonal wavelets were adapted to the interval [0,1) by Cohen et al. [7].  ... 
doi:10.1016/j.amc.2006.05.104 fatcat:kmpvq3nlljg3rp3a43ool3pyli

Lifting scheme for biorthogonal multiwavelets originated from Hermite splines

A.Z. Averbuch, V.A. Zheludev
2002 IEEE Transactions on Signal Processing  
We use the cubic interpolatory Hermite splines as a predicting aggregate in the vector wavelet transform.  ...  As a result, we get fast biorthogonal algorithms to transform discrete-time signals that are exact on sampled cubic polynomials. The bases for the transform are symmetric and have short support.  ...  In order to implement a vector wavelet transform, which is based on cubic Hermite splines, we need to have coefficients that are samples from the signal and its derivatives.  ... 
doi:10.1109/78.984720 fatcat:loam747ptvggzolk4de2bdys3m

Spaces of polynomial and nonpolynomial spline-wavelets

Yu. K. Dem'yanovich, I. G. Burova, T. O. Evdokimovas, A. V. Lebedeva, N. Mastorakis, V. Mladenov, A. Bulucea
2019 MATEC Web of Conferences  
This paper, discusses spaces of polynomial and nonpolynomial splines suitable for solving the Hermite interpolation problem (with first-order derivatives) and for constructing a wavelet decomposition.  ...  Also we construct a splash decomposition of the Hermitian type splines on a non-uniform grid.  ...  In particular, they obtain wavelet bases with simple structures on the interval [0,1] from the Hermite cubic splines.  ... 
doi:10.1051/matecconf/201929204001 fatcat:papkjf64k5ei3i4hg2vvlfvqou

Page 3699 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Karimova, Construction of quadrature formulas for singular integrals with a Cauchy kernel by means of cubic Hermite splines (45-50, 135); V. I.  ...  Khodzhaniyazov, On the error of interpolation by cubic splines on a uniform grid (62-76, 136); E. A. Shamsiev, On invariant cubature formulas that contain derivatives (77-85, 136); F.  ... 

Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Aiping Wang, Li Li, Shuli Mei, Kexin Meng
2020 Mathematics  
By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation  ...  To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal  ...  Acknowledgments: The Shannon-Cosine wavelet function in this paper is an improved version based on our ealy work, and so all the authors would like to thank Guo Shujun and all our colleagues for their  ... 
doi:10.3390/math9010001 fatcat:cs3evzwbvffabd3ra5rkzw2spa

Page 327 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
(D-AACH-G; Aachen) Biorthogonal multiwavelets on the interval: cubic Hermite splines. (English summary) Constr. Approx. 16 (2000), no. 2, 221-259.  ...  This paper deals with the construction of biorthogonal multi- wavelets on the interval [0,1] which are generated by C', piece- wise Hermite cubics with the following properties: the primal multiresolution  ... 

"Lazy" Wavelets of Hermite Quintic Splines and a Splitting Algorithm

Boris M. Shumilov, Ulukbek S. Ymanov
2013 Universal Journal of Computational Mathematics  
In this article two new types of wavelet bases for Hermite quintic splines are offered.  ...  The algorithm of wavelet decomposition as the solution of three systems of the linear equations, from which one system is three-diagonal with strict diagonal domination and two other systems are four-diagonal  ...  Acknowledgements The reported study was partially supported by RFBR, research project No. 13-01-90900_mol_in_nr.  ... 
doi:10.13189/ujcmj.2013.010401 fatcat:gt65tzkdpza4hlzvmx6wngucsy

Page 7051 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
In this paper, the authors consider, though only for cubic splines, an alternative construction of boundary spline wavelets on an interval and investigate corresponding decomposition and recon- struction  ...  The main result is the description of a criterion which enables one to find a unique generalized cubic spline with iso- geometry, which solves an Hermite interpolation problem with 3 specific restrictions  ... 

Page 8027 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
defect based on a uniform net.  ...  7], the second author established an integral representation of cardinal splines which allowed him to develop a wavelet analysis in the space of continuous splines of power growth.  ... 

On Five-Diagonal Splitting for Cubic Spline Wavelets with Six Vanishing Moments on a Segment

Boris Shumilov
2021 WSEAS Transactions on Information Science and Applications  
In this study, we use the vanishing property of the first six moments for constructing a splitting algorithm for cubic spline wavelets.  ...  The originality of the study consists in obtaining implicit relations connecting the coefficients of the spline decomposition at the initial scale with the spline coefficients and wavelet coefficients  ...  Construction of cubic spline wavelets with six vanishing moments on an interval Let V L denotes a space of cubic splines of smoothness C 2 on a segment [a, b] with a uniform grid consisting of the nodes  ... 
doi:10.37394/23209.2020.17.19 fatcat:mzw3kbfrfjgdjjtjcsst2zenni

Page 1835 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
cubic splines on tri- angulations of separable quadrangulations (405—424); Alexander Petukhov [A. P.  ...  The author has previously investigated the L,-convergence of Lagrange interpolation polynomials on a real interval.  ... 

A Biorthogonal Hermite Cubic Spline Galerkin Method for Solving Fractional Riccati Equation

Haifa Bin Jebreen, Ioannis Dassios
2022 Mathematics  
To this end, biorthogonal Hermite cubic Spline scaling bases and their properties are introduced, and the fractional integral is represented based on these bases as an operational matrix.  ...  This paper is devoted to the wavelet Galerkin method to solve the Fractional Riccati equation.  ...  In this paper, we focus on the wavelet Galerkin method, which used biorthogonal Hermite cubic Spline scaling bases (BHCSSb) as a set of bases to solve the fractional Riccati equation (FRE) C D β 0 u(x)  ... 
doi:10.3390/math10091461 fatcat:77gegqykxfem5n7s6nv7mjte2q

Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

Xiaogang Ji, Jie Xue, Yan Yang, Xueming He
2014 Mathematical Problems in Engineering  
Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting.  ...  On the basis of Dyadic wavelet fairing algorithm (DWFA), arbitrary resolution wavelet fairing algorithm (ARWFA), and corresponding software, accuracy control of multiresolution fairing was studied for  ...  Acknowledgments This work was supported by "the National Natural Science  ... 
doi:10.1155/2014/912024 fatcat:jpxxrh6r5zelxf3j34dxwb5cti

Page 4970 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
One of them, a local interpolant s € C'[0, 1], called Hermite spline in tension, interpolates the values and the first derivative of f € C'f0, 1] MN) C4Lx:, x41) on an arbitrary partition of the inter-  ...  All of these biquadratic splines are derived by means of the tensor product of linear spaces of qua- dratic splines and their bases are given by so-called fundamental splines.” G.  ... 
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