Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1283444534
,
9781461407720
,
9781283444538
Series Statement:
Springer Proceedings in Mathematics 13
Content:
These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7{u2013}10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. 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. It contains a carefully refereed and edited selection of papers. Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research.¡ Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.¡ Marian Neamtu is Professor of Mathematics at Vanderbilt University, Nashville, TN.¡ Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University, Nashville, TN
Content:
These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7--10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the
Note:
Includes bibliographical references
,
International conference proceedings
,
Approximation Theory XIII:San Antonio 2010; Preface; Contents; List of Contributors; An Asymptotic Equivalence Between Two Frame Perturbation Theorems; 1 The Perturbation Theorems; 2 An Asymptotic Equivalence; References; Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants; References; Generalization of Polynomial Interpolation at Chebyshev Nodes; 1 Introduction; 2 Generalization of Chebyshev Nodes; 3 Lebesgue Functions; 4 Properties of Pairs of Auxiliary Functions; 5 Optimal Nodes for Lagrange Polynomial Interpolation; References
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Green's Functions: Taking Another Look at Kernel Approximation, Radial Basis Functions, and Splines1 Introduction; 2 Toward an Intuitive Interpretation of Native Spaces; 2.1 What is the Current Situation?; 2.2 Mercer's Theorem and Eigenvalue Problems; 2.3 Green's Functions and Eigenfunction Expansions; 2.4 Generalized Sobolev Spaces; 3 Flat Limits; 3.1 Infinitely Smooth RBFs; 3.2 Finitely Smooth RBFs; 4 Stable Computation; 4.1 An Eigenfunction Expansion for Gaussians; 4.2 The RBF-QR Algorithm; 5 Dimension Independent Error Bounds; 5.1 The Current Situation
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5.2 New Results on (Minimal) Worst-Case Weighted L2 Error6 Summary; References; Sparse Recovery Algorithms: Sufficient Conditions in Terms of Restricted Isometry Constants; 1 Introduction; 1.1 Basis Pursuit; 1.2 Iterative Hard Thresholding; 1.3 Compressive Sampling Matching Pursuit; 2 Restricted Isometry Constants; 3 Basis Pursuit; 4 Iterative Hard Thresholding; 5 Compressive Sampling Matching Pursuit; References; Lagrange Interpolation and New Asymptotic Formulae for the Riemann Zeta Function; 1 Introduction; 2 Lagrange Interpolation; 3 Asymptotic Behavior of the Interpolation Error
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4 Asymptotic Formulae for ζ(s)5 Lp(-1,1)-Asymptotics and Criteria for ζ(s)=0 and ζ(s)≠0; 6 Remarks; References; Active Geometric Wavelets; 1 Introduction; 2 Theoretical Background; 2.1 A Jackson Estimate for Piecewise Polynomial Approximation Using Non-convex Domains; 2.2 Adaptive Local Selection of the Weight μ; 3 Overview of the AGW Algorithm; 4 Experimental Results; References; Interpolating Composite Systems; 1 Introduction; 2 Composite Dilation Systems; 3 Interpolating Systems; 4 Shearlets; 5 Conclusion; References
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Wavelets and Framelets Within the Framework of Nonhomogeneous Wavelet Systems1 Introduction; 2 Nonhomogeneous Wavelet Systems in L2(Rd); 3 Frequency-Based Nonhomogeneous Dual Framelets in the Distribution Space; 4 Wavelets and Framelets in Function Spaces; 5 Wavelets and Framelets Derived from Filter Banks; 6 Discrete Framelet Transform and Its Basic Properties; 7 Directional Tight Framelets in L2(Rd) and Projection Method; References; Compactly Supported Shearlets; 1 Introduction; 1.1 Directional Representation Systems
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1.2 Anisotropic Features, Discrete Shearlet Systems, and Quest for Sparse Approximations
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9781461407713
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-1-4614-0772-0
URL:
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