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Wavelet bases of Hermite cubic splines on the interval

2006
*
Advances in Computational Mathematics
*

In this paper a pair

doi:10.1007/s10444-003-7609-5
fatcat:342hkgk57jdhtkhljvlrzej4ry
*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*...##
###
Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines

2006
*
Applied Mathematics and Computation
*

Introduction Here we shall construct

doi:10.1016/j.amc.2006.05.104
fatcat:kmpvq3nlljg3rp3a43ool3pyli
*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]. ...##
###
Lifting scheme for biorthogonal multiwavelets originated from Hermite splines

2002
*
IEEE Transactions on Signal Processing
*

We use

doi:10.1109/78.984720
fatcat:loam747ptvggzolk4de2bdys3m
*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. ...##
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Spaces of polynomial and nonpolynomial spline-wavelets

2019
*
MATEC Web of Conferences
*

This paper, discusses spaces

doi:10.1051/matecconf/201929204001
fatcat:papkjf64k5ei3i4hg2vvlfvqou
*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*. ...##
###
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

2020
*
Mathematics
*

By studying

doi:10.3390/math9010001
fatcat:cs3evzwbvffabd3ra5rkzw2spa
*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 ...##
###
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

2013
*
Universal Journal of Computational Mathematics
*

In this article two new types

doi:10.13189/ujcmj.2013.010401
fatcat:gt65tzkdpza4hlzvmx6wngucsy
*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. ...##
###
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

2021
*
WSEAS Transactions on Information Science and Applications
*

In this study, we use

doi:10.37394/23209.2020.17.19
fatcat:mzw3kbfrfjgdjjtjcsst2zenni
*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 ...##
###
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

2022
*
Mathematics
*

To this end, biorthogonal

doi:10.3390/math10091461
fatcat:77gegqykxfem5n7s6nv7mjte2q
*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) ...##
###
Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

2014
*
Mathematical Problems in Engineering
*

Secondly, in consideration

doi:10.1155/2014/912024
fatcat:jpxxrh6r5zelxf3j34dxwb5cti
*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 ...##
###
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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