Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
... 73–76 Paraunitary filter banks, 44–47 double shift orthogonality conditions, 45 example, 46–47 important features, 45–46 orthogonal, 45 polynomial, 45 PCA (piecewise constant approximation), Haar wavelets and, 32–38 box function in, ...
Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing) Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques Numerous ...
G. Donovan, J.S. Geronimo, D.P. Hardin, P.R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 27 (4) (1996) 1158–1192. T. Bedford, Hölder exponents and box dimension for ...
Recently there have been many developments and new applications of mathematical techniques for describing complex algebraic functions and analysing empirical continuous data derived from many different types of signal, for...
This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This...
Wavelets and Frames on the Four-Directional Mesh Charles K. Chui, Kurt Jetter, and Joachim Stöckler Abstract. Although the integer translates of a box spline on the fourdirectional mesh do not constitute a Riesz basis, yet this box ...
... application areas common to both wavelets and fractals is the coding of images. Wavelets have been used extensively in the coding of images. Fractals have also been used ... THEIR 83 5.2 The Self-Similarity Idea in Wavelets and Fractals 83.
The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance.
A Multigrid Tutorial, SIAM, Philadelphia. Carpenter, M., Gottlieb, D., and Abarbanel, S. 1991, "The Stability of Numerical Boundary Treatments for Compact High- Order Finte-Difference Schemes." ICASE Report No. 91-71.
This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models.