Ebook: Variational Theory of Splines

This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.

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This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.
Content:
Front Matter....Pages i-xvii
Splines in Hilbert Spaces....Pages 1-22
Reproducing Mappings and Characterization of Splines....Pages 23-52
General Convergence Techniques and Error Estimates for Interpolating Splines....Pages 53-67
Splines in Subspaces....Pages 69-96
Interpolating D M -Splines....Pages 97-134
Splines on Manifolds....Pages 135-155
Vector Splines....Pages 157-174
Tensor and Blending Splines....Pages 175-194
Optimal Approximation of Linear Operators....Pages 195-213
Classification of Spline Objects....Pages 215-227
??-Approximations and Data Compression....Pages 229-242
Algorithms for Optimal Smoothing Parameter....Pages 243-262
Back Matter....Pages 263-280

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This book is a systematic description of the variational theory of splines in Hilbert spaces. All central aspects are discussed in the general form: existence, uniqueness, characterization via reproducing mappings and kernels, convergence, error estimations, vector and tensor hybrids in splines, dimensional reducing (traces of splines onto manifolds), etc. All considerations are illustrated by practical examples. In every case the numerical algorithms for the construction of splines are demonstrated.
Content:
Front Matter....Pages i-xvii
Splines in Hilbert Spaces....Pages 1-22
Reproducing Mappings and Characterization of Splines....Pages 23-52
General Convergence Techniques and Error Estimates for Interpolating Splines....Pages 53-67
Splines in Subspaces....Pages 69-96
Interpolating D M -Splines....Pages 97-134
Splines on Manifolds....Pages 135-155
Vector Splines....Pages 157-174
Tensor and Blending Splines....Pages 175-194
Optimal Approximation of Linear Operators....Pages 195-213
Classification of Spline Objects....Pages 215-227
??-Approximations and Data Compression....Pages 229-242
Algorithms for Optimal Smoothing Parameter....Pages 243-262
Back Matter....Pages 263-280
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