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Look Inside Quasi-Interpolation

Quasi-Interpolation

$94.00 (C)

Part of Cambridge Monographs on Applied and Computational Mathematics

Authors:
Martin Buhmann, Justus-Liebig-Universität Giessen, Germany
Janin Jäger, Justus-Liebig-Universität Giessen, Germany

Date Published: March 2022
availability: Available
format: Hardback
isbn: 9781107072633

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About the Authors

Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to suit applications in physics and engineering.
- Provides an in-depth summary of approximations using quasi-interpolation
- Explains the advantages of several different approaches to quasi-interpolation, including different convergence properties, smoothness and precision of approximants
- Offers a large range of examples and practical applications of quasi-interpolants, including scattered data, uniform data, solving PDEs and data compression
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Reviews & endorsements
'… the overall exposition and references make this book a potentially useful reference and an appropriate starting point for an advanced graduate student or researcher interested in studying the subject.' Edward J. Fuselier, MathSciNet

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Product details
- Date Published: March 2022
- format: Hardback
- isbn: 9781107072633
- length: 300 pages
- dimensions: 250 x 175 x 21 mm
- weight: 0.66kg
- availability: Available
Table of Contents
1. Introduction
2. Generalities on quasi-interpolation
3. Univariate RBF quasi-interpolants
4. Spline quasi-interpolants
5. Quasi-interpolants for periodic functions
6. Multivariate spline quasi-interpolants
7. Multivariate quasi-interpolants: construction in n dimensions
8. Quasi-interpolation on the sphere
9. Other quasi-interpolants and wavelets
10. Special cases and applications
References
Index.
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Authors
Martin Buhmann, Justus-Liebig-Universität Giessen, Germany
Martin D. Buhmann is Professor in the Mathematics Department at Justus Liebig University Giessen. He is the author of over 100 papers in numerical analysis, approximation theory, optimisation and differential equations, and of the monograph Radial Basis Functions: Theory and Implementations (Cambridge, 2003).
Janin Jäger, Justus-Liebig-Universität Giessen, Germany
Janin Jäger is Postdoctoral Fellow in the Mathematics Department at Justus Liebig University Giessen. Her research focuses on approximation theory using radial basis functions and their application to spherical data and neurophysiology.