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Author: Gregory E. Fasshauer
Publisher: Springer
ISBN: 3319064045
Category : Mathematics
Languages : en
Pages : 397
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Book Description
These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Author: Gregory E. Fasshauer
Publisher: Springer
ISBN: 3319064045
Category : Mathematics
Languages : en
Pages : 397
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Book Description
These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Author: Gregory E. Fasshauer
Publisher: Springer
ISBN: 3319599127
Category : Mathematics
Languages : en
Pages : 401
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Book Description
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.
Author: Christopher Beattie
Publisher: Springer Nature
ISBN: 303095157X
Category : Science
Languages : en
Pages : 462
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Book Description
This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.
Author: Stephan Dahlke
Publisher: Springer
ISBN: 3319081594
Category : Mathematics
Languages : en
Pages : 446
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Book Description
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Author: Yuesheng Xu
Publisher: American Mathematical Soc.
ISBN: 1470435500
Category : Mathematics
Languages : en
Pages : 134
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Book Description
This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .
Author: Philipp Grohs
Publisher: Springer Nature
ISBN: 3030313514
Category : Mathematics
Languages : en
Pages : 703
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Book Description
This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
Author: Stephan Dahlke
Publisher: Birkhäuser
ISBN: 3319188631
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.
Author: Yeonhyang Kim
Publisher: American Mathematical Soc.
ISBN: 1470436191
Category : Education
Languages : en
Pages : 358
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Book Description
This volume contains the proceedings of the AMS Special Sessions on Frames, Wavelets and Gabor Systems and Frames, Harmonic Analysis, and Operator Theory, held from April 16-17, 2016, at North Dakota State University in Fargo, North Dakota. The papers appearing in this volume cover frame theory and applications in three specific contexts: frame constructions and applications, Fourier and harmonic analysis, and wavelet theory.
Author:
Publisher: Elsevier
ISBN: 0444640045
Category : Mathematics
Languages : en
Pages : 712
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Book Description
Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. - About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization - Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading - The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs
Author: Jyotirmoy V. Deshmukh
Publisher: Springer Nature
ISBN: 3031067738
Category : Computers
Languages : en
Pages : 848
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Book Description
This book constitutes the proceedings of the 14th International Symposium on NASA Formal Methods, NFM 2022, held in Pasadena, USA, during May 24-27, 2022. The 33 full and 6 short papers presented in this volume were carefully reviewed and selected from 118submissions. The volume also contains 6 invited papers. The papers deal with advances in formal methods, formal methods techniques, and formal methods in practice. The focus on topics such as interactive and automated theorem proving; SMT and SAT solving; model checking; use of machine learning and probabilistic reasoning in formal methods; formal methods and graphical modeling languages such as SysML or UML; usability of formal method tools and application in industry, etc.
