# Generalized Spline Wavelets

## Related Articles

- Generalized Cardinal B-Splines: Stability, Linear Independence, and Appropriate Scaling Matrices. Dahlke, S.; Latour, V.; Neeb, M. // Constructive Approximation;1997, Vol. 13 Issue 1, p29
Generalized cardinal B-splines are defined as convolution products of characteristic functions of self-affine lattice tiles with respect to a given integer scaling matrix. By construction, these generalized splines are refinable functions with respect to the scaling matrix and therefore they can...

- A Class of Orthogonal Refinable Functions and Wavelets. Goodman, Tim N.T. // Constructive Approximation;2003, Vol. 19 Issue 4, p525
We give a construction, for any n â‰¥ 2, of a space S of spline functions of degree n - 1 with simple knots in Â¼ Z which is generated by a triple of refinable, orthogonal functions with compact support. Indeed, the result holds more generally by replacing the B-spline of degree n - 1 with...

- Spline-wavelet decompositions on manifolds. Dem�yanovich, Yu. // Journal of Mathematical Sciences;Apr2008, Vol. 150 Issue 1, p1787
We construct wavelet decompositions of the spline space on a smooth manifold. For this purpose, framed families of sets of fixed mutliplicity of covering and the corresponding approximation relations are introduced. We compute a calibration matrix and the left inverse matrix which are used to...

- On wavelet decomposition of spaces of first order splines. Makarov, A. // Journal of Mathematical Sciences;Jan2009, Vol. 156 Issue 4, p617
We consider approximate relations in the form of a system of linear algebraic equations that yield B f-splines. We construct Lagrange type splines of the first order and give examples of polynomial, trigonometric, hyperbolic, and exponential B f-splines. We also construct a system of linear...

- Surface Compression Using a Space of C1 Cubic Splines with a Hierarchical Basis. Hong, D.; Schumaker, L. L. // Computing;2004, Vol. 72 Issue 1/2, p79
A method for compressing surfaces associated with C1 cubic splines defined on triangulated quadrangulations is described. The method makes use of hierarchical bases, and does not require the construction of wavelets.

- Computing the Hilbert transform using biorthogonal spline wavelets. Martin, F.; Wegert, E. // Journal of Mathematical Sciences;Feb2013, Vol. 189 Issue 1, p150
In this paper, we summarize some facts on spline wavelets, analyze the Hilbert transform of these wavelets on the real line and on the unit circle, describe an algorithm for computing the Hilbert transform on uniform grids, and report on some test calculations.

- Numerical Solution of the Two Point Boundary Value Problems By Using Wavelet Bases of Hermite Cubic Spline Wavelets. Yousefi, Mehdi; Gherjalar, Hesam-Aldien Derili; Arzhang, Asghar // Australian Journal of Basic & Applied Sciences;2011, Vol. 5 Issue 12, p2098
In this paper, compactly supported Hermite cubic spline wavelets are developed to approximate the solutions of the linear two point boundary value problems. These wavelets constructed and properties of these wavelets utilized to reduce the computation of integral equations to some algebraic...

- On Non-Symmetric Orthogonal Spline Wavelets. Fukuda, N.; Kinoshita, T. // Southeast Asian Bulletin of Mathematics;2012, Vol. 36 Issue 3, p319
Orthogonal spline wavelets are usually symmetric or anti-symmetric. The Haar wavelet is the simplest type of wavelet. While, explicit formulas for higher order spline wavelets become complicated due to the orthogonality and also the symmetricity. In this paper, we shall consider non-symmetric...

- Properties of Decomposition Operators of Spline-Wavelet Decompositions. Dem'yanovich, Yu.; Burova, I. // Journal of Mathematical Sciences;Feb2015, Vol. 205 Issue 2, p205
We consider second order spline-wavelet decompositions and prove that the decomposition operators are independent of the order of removing certain grid nodes. We introduce the notion of a k-localized system of functionals and extract the set of operators containing only one left inverse of an...