Spherical Radial Basis Functions Theory And Applications

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Spherical Radial Basis Functions, Theory and Applications

Simon Hubbert,Quôc Thông Le Gia,Tanya M. Morton
Spherical Radial Basis Functions Theory and Applications Book PDF

Author : Simon Hubbert,Quôc Thông Le Gia,Tanya M. Morton
Publisher : Springer
Page : 143 pages
File Size : 42,8 Mb
Release : 2015-05-13
Category : Mathematics
ISBN : 9783319179391

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Spherical Radial Basis Functions, Theory and Applications by Simon Hubbert,Quôc Thông Le Gia,Tanya M. Morton Pdf

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.

Radial Basis Functions

Martin D. Buhmann
Radial Basis Functions Book PDF

Author : Martin D. Buhmann
Publisher : Cambridge University Press
Page : 271 pages
File Size : 40,6 Mb
Release : 2003-07-03
Category : Mathematics
ISBN : 9781139435246

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Radial Basis Functions by Martin D. Buhmann Pdf

The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence

Multivariate Algorithms and Information-Based Complexity

Fred J. Hickernell,Peter Kritzer
Multivariate Algorithms and Information Based Complexity Book PDF

Author : Fred J. Hickernell,Peter Kritzer
Publisher : Walter de Gruyter GmbH & Co KG
Page : 158 pages
File Size : 48,6 Mb
Release : 2020-06-08
Category : Mathematics
ISBN : 9783110635461

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Multivariate Algorithms and Information-Based Complexity by Fred J. Hickernell,Peter Kritzer Pdf

The contributions by leading experts in this book focus on a variety of topics of current interest related to information-based complexity, ranging from function approximation, numerical integration, numerical methods for the sphere, and algorithms with random information, to Bayesian probabilistic numerical methods and numerical methods for stochastic differential equations.

A Primer on Radial Basis Functions with Applications to the Geosciences

Bengt Fornberg,Natasha Flyer
A Primer on Radial Basis Functions with Applications to the Geosciences Book PDF

Author : Bengt Fornberg,Natasha Flyer
Publisher : SIAM
Page : 221 pages
File Size : 41,9 Mb
Release : 2015-09-30
Category : Science
ISBN : 9781611974041

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A Primer on Radial Basis Functions with Applications to the Geosciences by Bengt Fornberg,Natasha Flyer Pdf

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

Willi Freeden,Volker Michel
Multiscale Potential Theory Book PDF

Author : Willi Freeden,Volker Michel
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220480

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Multiscale Potential Theory by Willi Freeden,Volker Michel Pdf

This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.

Discrete Optimization and Operations Research

Yury Kochetov,Michael Khachay,Vladimir Beresnev,Evgeni Nurminski,Panos Pardalos
Discrete Optimization and Operations Research Book PDF

Author : Yury Kochetov,Michael Khachay,Vladimir Beresnev,Evgeni Nurminski,Panos Pardalos
Publisher : Springer
Page : 586 pages
File Size : 51,8 Mb
Release : 2016-09-09
Category : Computers
ISBN : 9783319449142

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Discrete Optimization and Operations Research by Yury Kochetov,Michael Khachay,Vladimir Beresnev,Evgeni Nurminski,Panos Pardalos Pdf

This book constitutes the proceedings of the 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, held in Vladivostok, Russia, in September 2016. The 39 full papers presented in this volume were carefully reviewed and selected from 181 submissions. They were organized in topical sections named: discrete optimization; scheduling problems; facility location; mathematical programming; mathematical economics and games; applications of operational research; and short communications.

Spherical Functions of Mathematical Geosciences

Willi Freeden,Michael Schreiner
Spherical Functions of Mathematical Geosciences Book PDF

Author : Willi Freeden,Michael Schreiner
Publisher : Springer Nature
Page : 729 pages
File Size : 51,8 Mb
Release : 2022
Category : Earth sciences
ISBN : 9783662656921

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Spherical Functions of Mathematical Geosciences by Willi Freeden,Michael Schreiner Pdf

This book is an enlarged second edition of a monograph published in the Springer AGEM2-Series, 2009. It presents, in a consistent and unified overview, a setup of the theory of spherical functions of mathematical (geo-)sciences. The content shows a twofold transition: First, the natural transition from scalar to vectorial and tensorial theory of spherical harmonics is given in a coordinate-free context, based on variants of the addition theorem, Funk-Hecke formulas, and Helmholtz as well as Hardy-Hodge decompositions. Second, the canonical transition from spherical harmonics via zonal (kernel) functions to the Dirac kernel is given in close orientation to an uncertainty principle classifying the space/frequency (momentum) behavior of the functions for purposes of data analysis and (geo-)application. The whole palette of spherical functions is collected in a well-structured form for modeling and simulating the phenomena and processes occurring in the Earth's system. The result is a work which, while reflecting the present state of knowledge in a time-related manner, claims to be of largely timeless significance in (geo-)mathematical research and teaching.

Quasi-Interpolation

Martin Buhmann,Martin D. Buhmann,Janin Jäger
Quasi Interpolation Book PDF

Author : Martin Buhmann,Martin D. Buhmann,Janin Jäger
Publisher : Cambridge University Press
Page : 291 pages
File Size : 40,9 Mb
Release : 2022-03-03
Category : Computers
ISBN : 9781107072633

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Quasi-Interpolation by Martin Buhmann,Martin D. Buhmann,Janin Jäger Pdf

Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.

Meshfree Approximation Methods with Matlab

Gregory E Fasshauer
Meshfree Approximation Methods with Matlab Book PDF

Author : Gregory E Fasshauer
Publisher : World Scientific Publishing Company
Page : 520 pages
File Size : 43,7 Mb
Release : 2007-04-17
Category : Mathematics
ISBN : 9789813101579

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Meshfree Approximation Methods with Matlab by Gregory E Fasshauer Pdf

Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.

Meshfree Approximation Methods with MATLAB

Gregory E. Fasshauer
Meshfree Approximation Methods with MATLAB Book PDF

Author : Gregory E. Fasshauer
Publisher : World Scientific
Page : 520 pages
File Size : 49,5 Mb
Release : 2007
Category : Technology & Engineering
ISBN : 9789812706331

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Meshfree Approximation Methods with MATLAB by Gregory E. Fasshauer Pdf

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

Arieh Iserles
Acta Numerica 2000 Volume 9 Book PDF

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 380 pages
File Size : 44,8 Mb
Release : 2000-07-13
Category : Mathematics
ISBN : 0521780373

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Acta Numerica 2000: Volume 9 by Arieh Iserles Pdf

An annual volume presenting substantive survey articles in numerical analysis and scientific computing.

Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

Kendall Atkinson,Weimin Han
Spherical Harmonics and Approximations on the Unit Sphere An Introduction Book PDF

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 48,6 Mb
Release : 2012-02-17
Category : Mathematics
ISBN : 9783642259821

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Spherical Harmonics and Approximations on the Unit Sphere: An Introduction by Kendall Atkinson,Weimin Han Pdf

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

Anonim
Issues in Logic Probability Combinatorics and Chaos Theory 2011 Edition Book PDF

Author : Anonim
Publisher : ScholarlyEditions
Page : 461 pages
File Size : 51,5 Mb
Release : 2012-01-09
Category : Mathematics
ISBN : 9781464966170

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Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2011 Edition by Anonim Pdf

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

Feng Dai,Yuan Xu
Approximation Theory and Harmonic Analysis on Spheres and Balls Book PDF

Author : Feng Dai,Yuan Xu
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 49,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781461466604

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Approximation Theory and Harmonic Analysis on Spheres and Balls by Feng Dai,Yuan Xu Pdf

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.

Theory and Application of Uniform Experimental Designs

Kai-Tai Fang,Min-Qian Liu,Hong Qin,Yong-Dao Zhou
Theory and Application of Uniform Experimental Designs Book PDF

Author : Kai-Tai Fang,Min-Qian Liu,Hong Qin,Yong-Dao Zhou
Publisher : Springer
Page : 300 pages
File Size : 48,7 Mb
Release : 2018-10-02
Category : Mathematics
ISBN : 9789811320415

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Theory and Application of Uniform Experimental Designs by Kai-Tai Fang,Min-Qian Liu,Hong Qin,Yong-Dao Zhou Pdf

The book provides necessary knowledge for readers interested in developing the theory of uniform experimental design. It discusses measures of uniformity, various construction methods of uniform designs, modeling techniques, design and modeling for experiments with mixtures, and the usefulness of the uniformity in block, factorial and supersaturated designs. Experimental design is an important branch of statistics with a long history, and is extremely useful in multi-factor experiments. Involving rich methodologies and various designs, it has played a key role in industry, technology, sciences and various other fields. A design that chooses experimental points uniformly scattered on the domain is known as uniform experimental design, and uniform experimental design can be regarded as a fractional factorial design with model uncertainty, a space-filling design for computer experiments, a robust design against the model specification, and a supersaturated design and can be applied to experiments with mixtures.