Quasi-Interpolation

Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.

Martin Buhmann (Author), Janin Jäger (Author)

9781107072633, Cambridge University Press

Hardback, published 3 March 2022

300 pages
25 x 17.5 x 2.1 cm, 0.66 kg

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.

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.

Subject Areas: Mathematical theory of computation [UYA], Information technology: general issues [UB], Numerical analysis [PBKS]