Spherical Radial Basis Functions Theory And Applications
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Spherical Radial Basis Functions Theory And Applications
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Author : Simon Hubbert
language : en
Publisher: Springer
Release Date : 2015-05-13
Spherical Radial Basis Functions Theory And Applications written by Simon Hubbert and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-13 with Mathematics categories.
This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.
A Primer On Radial Basis Functions With Applications To The Geosciences
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Author : Bengt Fornberg
language : en
Publisher: SIAM
Release Date : 2015-09-30
A Primer On Radial Basis Functions With Applications To The Geosciences written by Bengt Fornberg and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-30 with Science categories.
?Adapted from a series of lectures given by the authors, this monograph focuses on radial basis functions (RBFs), a powerful numerical methodology for solving PDEs to high accuracy in any number of dimensions. This method applies to problems across a wide range of PDEs arising in fluid mechanics, wave motions, astro- and geosciences, mathematical biology, and other areas and has lately been shown to compete successfully against the very best previous approaches on some large benchmark problems. Using examples and heuristic explanations to create a practical and intuitive perspective, the authors address how, when, and why RBF-based methods work.? The authors trace the algorithmic evolution of RBFs, starting with brief introductions to finite difference (FD) and pseudospectral (PS) methods and following a logical progression to global RBFs and then to RBF-generated FD (RBF-FD) methods. The RBF-FD method, conceived in 2000, has proven to be a leading candidate for numerical simulations in an increasingly wide range of applications, including seismic exploration for oil and gas, weather and climate modeling, and electromagnetics, among others.? This is the first survey in book format of the RBF-FD methodology and is suitable as the text for a one-semester first-year graduate class.
Multiscale Potential Theory
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Author : Willi Freeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiscale Potential Theory written by Willi Freeden 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.
During the last few decades, the subject of potential theory has not been overly popular in the mathematics community. Neglected in favor of more abstract theories, it has been taught primarily where instructors have ac tively engaged in research in this field. This situation has resulted in a scarcity of English language books of standard shape, size, and quality covering potential theory. The current book attempts to fill that gap in the literature. Since the rapid development of high-speed computers, the remarkable progress in highly advanced electronic measurement concepts, and, most of all, the significant impact of satellite technology, the flame of interest in potential theory has burned much brighter. The realization that more and more details of potential functions are adequately visualized by "zooming in" procedures of modern approximation theory has added powerful fuel to the flame. It seems as if, all of a sudden, harmonic kernel functions such as splines and/or wavelets provide the impetus to offer appropriate means of assimilating and assessing the readily increasing flow of potential data, reducing it to comprehensible form, and providing an objective basis for scientific interpretation, classification, testing of concepts, and solutions of problems involving the Laplace operator.
Meshfree Approximation Methods With Matlab
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Author : Gregory E. Fasshauer
language : en
Publisher: World Scientific
Release Date : 2007
Meshfree Approximation Methods With Matlab written by Gregory E. Fasshauer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.
Acta Numerica 2000 Volume 9
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-13
Acta Numerica 2000 Volume 9 written by Arieh Iserles 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 2000-07-13 with Mathematics categories.
An annual volume presenting substantive survey articles in numerical analysis and scientific computing.
Spherical Harmonics And Approximations On The Unit Sphere An Introduction
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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-02-17
Spherical Harmonics And Approximations On The Unit Sphere An Introduction written by Kendall Atkinson 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 2012-02-17 with Mathematics categories.
These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.
Issues In Logic Probability Combinatorics And Chaos Theory 2011 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09
Issues In Logic Probability Combinatorics And Chaos Theory 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.
Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Probability, Combinatorics, and Chaos Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Probability, Combinatorics, and Chaos Theory in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Approximation Theory And Harmonic Analysis On Spheres And Balls
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Author : Feng Dai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Approximation Theory And Harmonic Analysis On Spheres And Balls written by Feng Dai 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 2013-04-17 with Mathematics categories.
This monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Contemporary Computational Mathematics A Celebration Of The 80th Birthday Of Ian Sloan
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Author : Josef Dick
language : en
Publisher: Springer
Release Date : 2018-05-23
Contemporary Computational Mathematics A Celebration Of The 80th Birthday Of Ian Sloan written by Josef Dick and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-23 with Mathematics categories.
This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Geometric Algebra Applications Vol I
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Author : Eduardo Bayro-Corrochano
language : en
Publisher: Springer
Release Date : 2018-06-20
Geometric Algebra Applications Vol I written by Eduardo Bayro-Corrochano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-20 with Technology & Engineering categories.
The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.