Quasi-Interpolation

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.

'… 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