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Kernel Based Approximation Methods Using Matlab

Author: Gregory Fasshauer
Publisher: World Scientific Publishing Company
ISBN: 9814630152
Size: 24.52 MB
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In an attempt to introduce application scientists and graduate students to the exciting topic of positive definite kernels and radial basis functions, this book presents modern theoretical results on kernel-based approximation methods and demonstrates their implementation in various settings. The authors explore the historical context of this fascinating topic and explain recent advances as strategies to address long-standing problems. Examples are drawn from fields as diverse as function approximation, spatial statistics, boundary value problems, machine learning, surrogate modeling and finance. Researchers from those and other fields can recreate the results within using the documented MATLAB code, also available through the online library. This combination of a strong theoretical foundation and accessible experimentation empowers readers to use positive definite kernels on their own problems of interest.

Approximation Theory Xv San Antonio 2016

Author: Gregory E. Fasshauer
Publisher: Springer
ISBN: 3319599127
Size: 80.53 MB
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These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.

Digital Twin Technologies And Smart Cities

Author: Maryam Farsi
Publisher: Springer
ISBN: 3030187322
Size: 18.30 MB
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This book provides a holistic perspective on Digital Twin (DT) technologies, and presents cutting-edge research in the field. It assesses the opportunities that DT can offer for smart cities, and covers the requirements for ensuring secure, safe and sustainable smart cities. Further, the book demonstrates that DT and its benefits with regard to: data visualisation, real-time data analytics, and learning leading to improved confidence in decision making; reasoning, monitoring and warning to support accurate diagnostics and prognostics; acting using edge control and what-if analysis; and connection with back-end business applications hold significant potential for applications in smart cities, by employing a wide range of sensory and data-acquisition systems in various parts of the urban infrastructure. The contributing authors reveal how and why DT technologies that are used for monitoring, visualising, diagnosing and predicting in real-time are vital to cities sustainability and efficiency. The concepts outlined in the book represents a city together with all of its infrastructure elements, which communicate with each other in a complex manner. Moreover, securing Internet of Things (IoT) which is one of the key enablers of DTs is discussed in details and from various perspectives. The book offers an outstanding reference guide for practitioners and researchers in manufacturing, operations research and communications, who are considering digitising some of their assets and related services. It is also a valuable asset for graduate students and academics who are looking to identify research gaps and develop their own proposals for further research.

Approximation Theory And Algorithms For Data Analysis

Author: Armin Iske
Publisher: Springer
ISBN: 3030052281
Size: 54.43 MB
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This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.

Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science

Author: Isaac Pesenson
Publisher: Birkhäuser
ISBN: 3319555561
Size: 61.39 MB
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The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Meshfree Approximation Methods With Matlab

Author: Gregory E. Fasshauer
Publisher: World Scientific
ISBN: 981270633X
Size: 52.92 MB
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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.

Machine Learning With Svm And Other Kernel Methods

Author: K.P. Soman
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120334353
Size: 57.57 MB
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Support vector machines (SVMs) represent a breakthrough in the theory of learning systems. It is a new generation of learning algorithms based on recent advances in statistical learning theory. Designed for the undergraduate students of computer science and engineering, this book provides a comprehensive introduction to the state-of-the-art algorithm and techniques in this field. It covers most of the well known algorithms supplemented with code and data. One Class, Multiclass and hierarchical SVMs are included which will help the students to solve any pattern classification problems with ease and that too in Excel. KEY FEATURES  Extensive coverage of Lagrangian duality and iterative methods for optimization  Separate chapters on kernel based spectral clustering, text mining, and other applications in computational linguistics and speech processing  A chapter on latest sequential minimization algorithms and its modifications to do online learning  Step-by-step method of solving the SVM based classification problem in Excel.  Kernel versions of PCA, CCA and ICA The CD accompanying the book includes animations on solving SVM training problem in Microsoft EXCEL and by using SVMLight software . In addition, Matlab codes are given for all the formulations of SVM along with the data sets mentioned in the exercise section of each chapter.

Computer Based Exercises For Signal Processing Using Matlab 5

Author: James H. McClellan
Publisher:
ISBN:
Size: 60.31 MB
Format: PDF, Kindle
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FEATURES: bull; bull;Presents many computer-based problems that can be done in conjunction with a course in DSP theory. bull; bull;Projects relate to practical systems and implementations so the reader can learn and understand how DSP is applied. bull;Includes projects and exercises, which make full use of the power of MATLAB v5 to explore conceptual, analytical, and computational issues in digital signal processing. bull;Many projects provide hints to introduce pitfalls, limitations and tricks for getting the most out of MATLAB v5. bull;Discusses both the power and limitations of MATLAB v5 functions and regularly explores the issue of using built-in functions versus developing code to solve problems. bull;Exercises consistently reinforce important problem solving behaviors, such as verifying results, experimenting with parameters as a means of building understanding and intuition, exploring the realism of formulations, comparing theoretical and numerical or measured results, and developing predictions and then comparing them to actual results.