Del 37 i serien Cambridge Monographs on Applied and Computational Mathematics

Quasi-Interpolation

Inbunden, Engelska, 2022

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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.

Produktinformation

Utgivningsdatum2022-03-03
Mått175 x 250 x 21 mm
Vikt660 g
FormatInbunden
SpråkEngelska
SerieCambridge Monographs on Applied and Computational Mathematics
Antal sidor290
FörlagCambridge University Press
ISBN9781107072633

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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 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.

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.