Quasi-interpolation
著者
書誌事項
Quasi-interpolation
（Cambridge monographs on applied and computational mathematics, 37）
Cambridge University Press, c2022
- :hbk.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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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