Ridge Functions
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Ridge Functions
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Author : Allan Pinkus
language : en
Publisher: Cambridge University Press
Release Date : 2015-08-07
Ridge Functions written by Allan Pinkus and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-07 with Computers categories.
Presents the state of the art in the theory of ridge functions, providing a solid theoretical foundation.
Ridge Functions And Applications In Neural Networks
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Author : Vugar E. Ismailov
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-17
Ridge Functions And Applications In Neural Networks written by Vugar E. Ismailov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-17 with Mathematics categories.
Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.
Beyond Wavelets
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Author : Grant Welland
language : en
Publisher: Academic Press
Release Date : 2003-09-08
Beyond Wavelets written by Grant Welland and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-09-08 with Mathematics categories.
"Beyond Wavelets" presents state-of-the-art theories, methods, algorithms, and applications of mathematical extensions for classical wavelet analysis. Wavelets, introduced 20 years ago by Morlet and Grossmann and developed very rapidly during the 1980's and 1990's, has created a common link between computational mathematics and other disciplines of science and engineering. Classical wavelets have provided effective and efficient mathematical tools for time-frequency analysis which enhances and replaces the Fourier approach. However, with the current advances in science and technology, there is an immediate need to extend wavelet mathematical tools as well. "Beyond Wavelets" presents a list of ideas and mathematical foundations for such extensions, including: continuous and digital ridgelets, brushlets, steerable wavelet packets, contourlets, eno-wavelets, spline-wavelet frames, and quasi-affine wavelets. Wavelet subband algorithms are extended to pyramidal directional and nonuniform filter banks. In addition, this volume includes a method for tomographic reconstruction using a mechanical image model and a statistical study for independent adaptive signal representation. Investigators already familiar with wavelet methods from areas such as engineering, statistics, and mathematics will benefit by owning this volume. *Curvelets, Contourlets, Ridgelets, *Digital Implementation of Ridgelet Packets *Steerable Wavelet Packets *Essentially Non-Oscillatory Wavelets *Medical Imaging *Non-Uniform Filter Banks *Spline-wavelet frames and *Vanishing Moment Recovery Functions
Approximation Theory Spline Functions And Applications
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Author : S.P. Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximation Theory Spline Functions And Applications written by S.P. Singh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
These are the Proceedings of the NATO Advanced Study Institute on Approximation Theory, Spline Functions and Applications held in the Hotel villa del Mare, Maratea, Italy between April 28,1991 and May 9, 1991. The principal aim of the Advanced Study Institute, as reflected in these Proceedings, was to bring together recent and up-to-date developments of the subject, and to give directions for future research. Amongst the main topics covered during this Advanced Study Institute is the subject of uni variate and multivariate wavelet decomposition over spline spaces. This is a relatively new area in approximation theory and an increasingly impor tant subject. The work involves key techniques in approximation theory cardinal splines, B-splines, Euler-Frobenius polynomials, spline spaces with non-uniform knot sequences. A number of scientific applications are also highlighted, most notably applications to signal processing and digital im age processing. Developments in the area of approximation of functions examined in the course of our discussions include approximation of periodic phenomena over irregular node distributions, scattered data interpolation, Pade approximants in one and several variables, approximation properties of weighted Chebyshev polynomials, minimax approximations, and the Strang Fix conditions and their relation to radial functions. I express my sincere thanks to the members of the Advisory Commit tee, Professors B. Beauzamy, E. W. Cheney, J. Meinguet, D. Roux, and G. M. Phillips. My sincere appreciation and thanks go to A. Carbone, E. DePas cale, R. Charron, and B.
Wavelets
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Author : B. W. Silverman
language : en
Publisher:
Release Date : 2000
Wavelets written by B. W. Silverman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
In recent years there has been an explosion of interest in wavelets, in a wide range of fields in science and engineering and beyond. This book brings together contributions from researchers from disparate fields, both in order to demonstrate to a wide readership the current breadth of work in wavelets, and to encourage cross-fertilization of ideas. It demonstrates the genuinely interdisplinary nature of wavelet research and applications. Particular areas covered include turbulence, statistics, time series analysis, signal and image processing, the physiology of vision, astronomy, economics and acoustics. Some of the work uses standard wavelet approaches and in other cases new methodology is developed. The papers were originally presented at a Royal Society Discussion Meeting, to a large and enthusiastic audience of specialists and non-specialists.
Recent Advances In Harmonic Analysis And Applications
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Author : Dmitriy Bilyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-16
Recent Advances In Harmonic Analysis And Applications written by Dmitriy Bilyk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-16 with Mathematics categories.
Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.
Novel Algorithms For Fast Statistical Analysis Of Scaled Circuits
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Author : Amith Singhee
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-08-14
Novel Algorithms For Fast Statistical Analysis Of Scaled Circuits written by Amith Singhee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-14 with Technology & Engineering categories.
As VLSI technology moves to the nanometer scale for transistor feature sizes, the impact of manufacturing imperfections result in large variations in the circuit performance. Traditional CAD tools are not well-equipped to handle this scenario, since they do not model this statistical nature of the circuit parameters and performances, or if they do, the existing techniques tend to be over-simplified or intractably slow. Novel Algorithms for Fast Statistical Analysis of Scaled Circuits draws upon ideas for attacking parallel problems in other technical fields, such as computational finance, machine learning and actuarial risk, and synthesizes them with innovative attacks for the problem domain of integrated circuits. The result is a set of novel solutions to problems of efficient statistical analysis of circuits in the nanometer regime.
Foundations Of Genetic Algorithms
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Author : Christopher R. Stephens
language : en
Publisher: Springer
Release Date : 2007-08-15
Foundations Of Genetic Algorithms written by Christopher R. Stephens and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-15 with Computers categories.
Readers will find here a fascinating text that is the thoroughly refereed post-proceedings of the 9th Workshop on the Foundations of Genetic Algorithms, FOGA 2007, held in Mexico City in January 2007. The 11 revised full papers presented were carefully reviewed and selected during two rounds of reviewing and improvement from 22 submissions. The papers address all current topics in the field of theoretical evolutionary computation and also depict the continuing growth in interactions with other fields such as mathematics, physics, and biology
Principles And Theory For Data Mining And Machine Learning
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Author : Bertrand Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-21
Principles And Theory For Data Mining And Machine Learning written by Bertrand Clarke and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-21 with Computers categories.
The idea for this book came from the time the authors spent at the Statistics and Applied Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina starting in fall 2003. The rst author was there for a total of two years, the rst year as a Duke/SAMSI Research Fellow. The second author was there for a year as a Post-Doctoral Scholar. The third author has the great fortune to be in RTP p- manently. SAMSI was – and remains – an incredibly rich intellectual environment with a general atmosphere of free-wheeling inquiry that cuts across established elds. SAMSI encourages creativity: It is the kind of place where researchers can be found at work in the small hours of the morning – computing, interpreting computations, and developing methodology. Visiting SAMSI is a unique and wonderful experience. The people most responsible for making SAMSI the great success it is include Jim Berger, Alan Karr, and Steve Marron. We would also like to express our gratitude to Dalene Stangl and all the others from Duke, UNC-Chapel Hill, and NC State, as well as to the visitors (short and long term) who were involved in the SAMSI programs. It was a magical time we remember with ongoing appreciation.
A Course In Approximation Theory
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Author : Elliott Ward Cheney
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-01-13
A Course In Approximation Theory written by Elliott Ward Cheney and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-13 with Mathematics categories.
This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.