Topics in Polynomial Interpolation Theory
Appears in the following Collection
- Matematikk 
AbstractThis thesis studies two aspects of polynomial interpolation theory. The first part sets forth explicit formulas for the coefficients of polynomial interpolants to implicit functions. A formula for the higher-order derivatives of implicit functions appears as a limiting case of these formulas. The second part delves into certain configurations of points in space — generalized principal lattices — that are well suited as interpolation points. Applying the theory of real algebraic curves then allows the construction of many new examples of such configurations.
List of papers
|Paper I / Chapter 2 Georg Muntingh and Michael Floater: Divided Differences of Univariate Implicit Functions Math. Comp. 80 (2011), 2185-2195 First published in Mathematics of Computation in volume 80 (2011), published by the American Mathematical Society https://doi.org/10.1090/S0025-5718-2011-02486-5|
|Paper II / Chapter 3 Georg Muntingh: Divided Differences of Multivariate Implicit Functions BIT Numerical Mathematics (2012) Published Online 29 February 2012. The original publication is available at www.springerlink.com https://doi.org/10.1007/s10543-012-0377-1|