Download or read book Scattered Data Approximation written by Holger Wendland and published by Cambridge University Press. This book was released on 2004-12-13 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to support courses in computer-aided geometric design, and meshless methods for partial differential equations.
Download or read book Multiresolution Methods in Scattered Data Modelling written by Armin Iske and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This application-oriented work concerns the design of efficient, robust and reliable algorithms for the numerical simulation of multiscale phenomena. To this end, various modern techniques from scattered data modelling, such as splines over triangulations and radial basis functions, are combined with customized adaptive strategies, which are developed individually in this work. The resulting multiresolution methods include thinning algorithms, multi levelapproximation schemes, and meshfree discretizations for transport equa tions. The utility of the proposed computational methods is supported by their wide range of applications, such as image compression, hierarchical sur face visualization, and multiscale flow simulation. Special emphasis is placed on comparisons between the various numerical algorithms developed in this work and comparable state-of-the-art methods. To this end, extensive numerical examples, mainly arising from real-world applications, are provided. This research monograph is arranged in six chapters: 1. Introduction; 2. Algorithms and Data Structures; 3. Radial Basis Functions; 4. Thinning Algorithms; 5. Multilevel Approximation Schemes; 6. Meshfree Methods for Transport Equations. Chapter 1 provides a preliminary discussion on basic concepts, tools and principles of multiresolution methods, scattered data modelling, multilevel methods and adaptive irregular sampling. Relevant algorithms and data structures, such as triangulation methods, heaps, and quadtrees, are then introduced in Chapter 2.
Download or read book Scattered Data Interpolation and Approximation written by Thomas Alfred Foley and published by . This book was released on 1984* with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattered Data Approximation on the Rotation Group and Generalizations written by Dominik Schmid and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Meshfree Approximation Methods with MATLAB written by Gregory E. Fasshauer and published by World Scientific. This book was released on 2007 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scattered Data Approximation Based on Delaunay Tessellation written by Kyoya Tsutsui and published by . This book was released on 1986 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scattered Data Approximation Using the Mask Method written by Berit Ingeborg Kvernes and published by . This book was released on 1994 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory and Spline Functions written by S.P. Singh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: A NATO Advanced Study Institute on Approximation Theory and Spline Functions was held at Memorial University of Newfoundland during August 22-September 2, 1983. This volume consists of the Proceedings of that Institute. These Proceedings include the main invited talks and contributed papers given during the Institute. The aim of these lectures was to bring together Mathematicians, Physicists and Engineers working in the field. The lectures covered a wide range including ~1ultivariate Approximation, Spline Functions, Rational Approximation, Applications of Elliptic Integrals and Functions in the Theory of Approximation, and Pade Approximation. We express our sincere thanks to Professors E. W. Cheney, J. Meinguet, J. M. Phillips and H. Werner, members of the International Advisory Committee. We also extend our thanks to the main speakers and the invi ted speakers, whose contri butions made these Proceedings complete. The Advanced Study Institute was financed by the NATO Scientific Affairs Division. We express our thanks for the generous support. We wish to thank members of the Department of Mathematics and Statistics at MeMorial University who willingly helped with the planning and organizing of the Institute. Special thanks go to Mrs. Mary Pike who helped immensely in the planning and organizing of the Institute, and to Miss Rosalind Genge for her careful and excellent typing of the manuscript of these Proceedings.
Download or read book Radial Basis Functions written by Martin D. Buhmann and published by Cambridge University Press. This book was released on 2003-07-03 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Operator Adapted Wavelets Fast Solvers and Numerical Homogenization written by Houman Owhadi and published by Cambridge University Press. This book was released on 2019-10-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.
Download or read book Geometric Modeling written by Hans Hagen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
Download or read book An Introduction to Sparse Stochastic Processes written by Michael Unser and published by Cambridge University Press. This book was released on 2014-08-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.
Download or read book Introduction to Ground Penetrating Radar written by Raffaele Persico and published by John Wiley & Sons. This book was released on 2014-06-09 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: A real-world guide to practical applications of ground penetrating radar (GPR) The nondestructive nature of ground penetrating radar makes it an important and popular method of subsurface imaging, but it is a highly specialized field, requiring a deep understanding of the underlying science for successful application. Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing provides experienced professionals with the background they need to ensure precise data collection and analysis. Written to build upon the information presented in more general introductory volumes, the book discusses the fundamental mathematical, physical, and engineering principles upon which GPR is built. Real-world examples and field data provide readers an accurate view of day-to-day GPR use. Topics include: 2D scattering for dielectric and magnetic targets 3D scattering equations and migration algorithms Host medium characterization and diffraction tomography Time and frequency steps in GPR data sampling The Born approximation and the singular value decomposition The six appendices contain the mathematical proofs of all examples discussed throughout the book. Introduction to Ground Penetrating Radar: Inverse Scattering and Data Processing is a comprehensive resource that will prove invaluable in the field.
Download or read book Approximation to Scattered Data by Radial Basis Function written by Jungho Yoon and published by . This book was released on 1998 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exact Constants in Approximation Theory written by Nikolaĭ Pavlovich Korneĭchuk and published by Cambridge University Press. This book was released on 1991-06-06 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.
Download or read book Boundary Effects in Scattered Data Approximation written by Sören Wolfers and published by . This book was released on 2015 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Linear Algebra written by William Layton and published by World Scientific. This book was released on 2020-07-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The numerical algorithms presented are written in pseudocode and based on MATLAB, a programming and numeric computing platform widely used in STEM fields. Thus, no formal training in computer science or knowledge of any specific programming language is needed to parse the algorithms. Summing up: Recommended.'CHOICEMany students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Each topic is presented as algorithmic ideas and through a foundation based on mostly applied analysis. By picking a path through the book appropriate for the level, it has been used for both senior level undergraduates and beginning graduate classes with students from diverse fields and backgrounds.
