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  3. Quasi-Interpolation
  • Cited by 14
Publisher:
Cambridge University Press
Online publication date:
February 2022
Print publication year:
2022
Online ISBN:
9781139680523
DOI:
https://doi.org/10.1017/9781139680523
Subjects:
Mathematics, Computational Science, Numerical Analysis and Computational Science
Series:
Cambridge Monographs on Applied and Computational Mathematics (37)
Information

Book description

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.

Reviews

'… 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 Source: MathSciNet

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