Approximation Theory XIV.
By: Fasshauer, Gregory E.
Contributor(s): Schumaker, Larry L.Material type: TextSeries: eBooks on Demand.Springer Proceedings in Mathematics & Statistics: Publisher: Dordrecht : Springer, 2014Description: 1 online resource (397 p.).ISBN: 9783319064048.Subject(s): Approximation theoryGenre/Form: Electronic books.Additional physical formats: Print version:: Approximation Theory XIV: San Antonio 2013DDC classification: 511 | 511.4 | 511/.4 Online resources: Click here to view this ebook.
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Preface; Contents; Contributors; 1 Isogeometric Method for the Elliptic Monge-Ampère Equation; 1 Introduction; 2 Notation and Preliminaries; 3 Minimization Results; 4 Isogeometric Analysis; 5 Numerical Results; References; 2 Dual Compatible Splines on Nontensor Product Meshes; 1 Introduction; 2 Preliminaries ; 3 Dual Compatible B-Splines; References; 3 Multivariate Anisotropic Interpolation on the Torus; 1 Introduction; 2 Preliminaries; 2.1 Patterns; 2.2 Function Spaces; 3 Interpolation and the Strang-Fix Condition; 4 Error Bounds for Interpolation; 5 The Three-Directional Box Splines
References4 A Generalized Class of Hard Thresholding Algorithms for Sparse Signal Recovery; 1 Compressive Sensing and Sparse Signal Recovery; 2 (HTP), (GHTP), and their Generalizations; 2.1 Previous Results; 2.2 Generalizations; 2.3 First Results; 3 Uniform Recovery via (f-HTP); 3.1 General Results; 3.2 The Case of Power Vectors; 4 Nonuniform Recovery via (f-HTP); 4.1 Useful Inequalities; 4.2 Recovery; 4.3 Hybrid Algorithms; 5 Numerical Results; 5.1 Successful Recovery and Area of Convergence; 5.2 Number of Iterations for Successful Recovery; 5.3 Indices Correctly Captured; 6 Conclusion
References5 On a New Proximity Condition for Manifold-Valued Subdivision Schemes; 1 Introduction; 2 Smooth Compatibility and the Differential Proximity Condition; 3 What's New?; 4 Coordinate Independence; 5 The Log-exp Scheme on Surfaces; References; 6 Wachspress and Mean Value Coordinates; 1 Introduction; 2 Barycentric Coordinates on Polygons; 3 Wachspress Coordinates; 3.1 Rational Functions; 3.2 Perpendicular Distances to Edges; 3.3 Gradients; 3.4 Curve Deformation; 4 Mean Value Coordinates; 4.1 Gradients; 4.2 Alternative Formula; 4.3 Star-Shaped Polygons; 4.4 Arbitrary Polygons
5 Polygonal Finite Elements6 Curved Domains; 6.1 Hermite Interpolation; 7 Coordinates in Higher Dimensions; 7.1 Wachspress Coordinates in 3D; 7.2 MV Coordinates in 3D; 8 Final Remarks; References; 7 Hermite and Bernstein Style Basis Functions for Cubic Serendipity Spaces on Squares and Cubes; 1 Introduction; 2 Background and Notation; 2.1 Serendipity Elements; 2.2 Cubic Bernstein and Hermite Bases; 3 Local Bases for mathcalS3(I2); 3.1 A Local Bernstein Style Basis for mathcalS3(I2); 3.2 A Local Hermite Style Basis for mathcalS3(I2); 4 Local Bases for mathcalS3(I3)
4.1 A Local Bernstein Style Basis for mathcalS3(I3)4.2 A Local Hermite Style Basis for mathcalS3(I3); 5 Conclusions and Future Directions; References; 8 Suitability of Parametric ShepardInterpolation for Nonrigid Image Registration; 1 Introduction; 2 Parametric Shepard Interpolation; 3 Evaluation; 4 Concluding Remarks; References; 9 Parabolic Molecules: Curvelets, Shearlets, and Beyond; 1 Introduction; 2 Representation of Multivariate Data; 2.1 Sparse Approximation; 2.2 Image Data and Anisotropic Phenomena; 2.3 2D Wavelet Systems; 3 Directional Representation Systems
3.1 Second-Generation Curvelets
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 incl
Description based upon print version of record.