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Additional affiliations
April 2013 - March 2014
March 2010 - May 2011
October 2009 - March 2014
Education
January 2009 - November 2012
July 2007 - December 2008
August 2006 - June 2007
Publications
Publications (5)
We present two partitioning algorithms that allow a sum of piecewise linear polynomials over a number of overlaying convex partitions of the unit cube Ω ∈ R^d to approximate a function f∈W^3_p(Ω) with the order N^{−6/(2d+1)} in Lp-norm, where N is the total number of cells of all partitions, which makes a marked improvement over the N^{−2/d} order...
The subject of this thesis includes the design of new partitioning methods for the approximation of a function f on a domain Ω ⊂ R^d, d ≥ 2 by piecewise linear functions, and the derivation of errors estimations in L_p-norm and W^1_p seminorm. In the two-dimensional setting, we develop a construction of a sequence of anisotropic triangulations, whe...
We present a full characterisation of interpolatory mask symbols where the dilation matrix is M = 2I. The characterization involves the analysis of polynomial identities in two variables by means of the Bezout theorem and the Euclidean algorithm. The convergence of the associated interpolatory subdivision scheme is closely related to the existence...
See full text for abstract. Thesis (MSc (Mathematics))--University of Stellenbosch, 2008.
In this essay, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalise metric spaces. In particular, the self-distance for any point needs not be equal to zero. The main part of this work concentrates on the theory of partial metric spaces by referring to their induced metric spaces. Working i...