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Author: Ognyan Kounchev
Publisher: Academic Press
ISBN: 0080525008
Category : Mathematics
Languages : en
Pages : 513
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Book Description
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property
Author: Ognyan Kounchev
Publisher: Academic Press
ISBN: 0080525008
Category : Mathematics
Languages : en
Pages : 513
Get Book Here
Book Description
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property
Author: Ognyan Kounchev
Publisher:
ISBN: 9780123909350
Category :
Languages : en
Pages : 498
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Book Description
Author: O. Kounchev
Publisher: IOS Press
ISBN: 1607502569
Category : Business & Economics
Languages : en
Pages : 360
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Book Description
Today’s security environment is characterized by deep uncertainty. Threats are being posed not only by adversary (political) forces but may also come from natural challenges (be it energy, water, ecology or whatever). The types of operations that our civil security and military forces find themselves in today comprise a wide variety of tasks. The success criteria for these operations are a safe/secure environment for local population and stable conditions for state building rather than hit-kill ratio’s against adversaries – the criteria are soft and the many actors involved may have divergent if not opposing objectives. And where actors intentionally share common objectives, they come from different cultural and organizational backgrounds, and their systems and modus operandi (doctrine) have loose or no connectivity. Under these complex and uncertain conditions decision making is a challenging process. This publication reflect the initial state of a dialogue between specialists in security and specialists in mathematics, computer and information sciences on security topics. Papers included in this volume are naturally subdivided into four parts showing the wide future perspective for synthesis between science and security: Planning for Security; Mathematical, Computer and Information Sciences Methods for Security; Environmental Security; and Dynamic Optimization for Security.
Author:
Publisher: IOS Press
ISBN:
Category :
Languages : en
Pages : 10439
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Book Description
Author: Jean-Daniel Boissonnat
Publisher: Springer
ISBN: 3319228048
Category : Computers
Languages : en
Pages : 502
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Book Description
This volume constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Curves and Surfaces, held in Paris, France, in June 2014. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 32 revised full papers presented were carefully reviewed and selected from 39 submissions. The scope of the conference was on following topics: approximation theory, computer-aided geometric design, computer graphics and visualization, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, mesh generation, finite elements and splines, scattered data processing and learning theory, sparse and high-dimensional approximation, subdivision, wavelets and multi-resolution method.
Author: Mark Lʹvovich Agranovskiĭ
Publisher: American Mathematical Soc.
ISBN: 0821841505
Category : Mathematics
Languages : en
Pages : 482
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Book Description
The papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.
Author: Gregory E Fasshauer
Publisher: World Scientific Publishing Company
ISBN: 9813101571
Category : Mathematics
Languages : en
Pages : 520
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Book Description
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.
Author: Gregory E. Fasshauer
Publisher: World Scientific
ISBN: 981270633X
Category : Technology & Engineering
Languages : en
Pages : 520
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Book Description
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.
Author: Michael J. Wilson
Publisher: Springer Science & Business Media
ISBN: 3540200533
Category : Computers
Languages : en
Pages : 401
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Book Description
This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.
Author: Gregory E Fasshauer
Publisher: World Scientific Publishing Company
ISBN: 9814630152
Category : Mathematics
Languages : en
Pages : 537
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Book Description
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.
