Constructive Approximation on the Sphere: (With an Emphasis on Geomathematics)

Hardcover | December 1, 1997

byMichael Schreiner, Willi Freeden, Theo Gervens

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The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this bookprovides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area.This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines andwavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to newstructures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.

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The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this bookprovides the necessary foundation for gradua...

Willi Freeden, Professor, Geomathematics Group, both at the University of Kaiserslauten. Theo Gervens, Professor, University of Osnabruck.

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Format:HardcoverDimensions:442 pages, 9.21 × 6.14 × 0.1 inPublished:December 1, 1997Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198536828

ISBN - 13:9780198536826

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Table of Contents

1. Notation2. Polynomials3. Scalar Spherical Harmonics4. Green's Functions5. Spherical Radial Basis Functions6. Spherical Splines7. Approximate Integration8. Spherical Singular Integrals9. Gabor and Toeplitz Transform10. Continuous Wavelet Transform11. Discrete Wavelet Transform12. Vector Spherical Harmonics13. Vectorial Approximation Methods14. Tensor Spherical Harmonics15. Tensorial Approximation MethodsReferencesSubject Index

Editorial Reviews

'This book provides an excellent modern resource for all workers interested in approximation on spherical geometrics ... it contains a very complete treatment of approximation techniques ... This book fills a large gap in the literature by giving a modern treatment of spherical approximationtechniques which starts from the first principles but reaches modern developments' Proceedings of the Edinburgh Mathematical Society