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Approximation Theory XIV.

By: Fasshauer, Gregory E.
Contributor(s): Schumaker, Larry L.
Material type: TextTextSeries: 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.
Contents:
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
Summary: 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
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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

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