6 citations · 22 across the 16 of their papers we have counts for
11 papers · 1 filter
Computing expected moments of the Rényi parking problem on the circle
Markus Hegland, Conrad J. Burden, Zbigniew Stachurski
A highly accurate and efficient method to compute the expected values of the count, sum, and squared norm of the sum of the centre vectors of a random maximal sized collection of n…
A Note on Error Bounds for Pseudo Skeleton Approximations of Matrices
Frank de Hoog, Markus Hegland
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices.…
Low rank approximation of positive semi-definite symmetric matrices using Gaussian elimination and volume sampling
Markus Hegland, Frank deHoog
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They a…
Scalable and Fault Tolerant Computation with the Sparse Grid Combination Technique
Brendan Harding, Markus Hegland, Jay Larson +1
This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C…
Convergence rates in -regularization when the basis is not smooth enough
Jens Flemming, Markus Hegland
Sparsity promoting regularization is an important technique for signal reconstruction and several other ill-posed problems. Theoretical investigation typically bases on the assumpt…
Sparse grid quadrature on products of spheres
Markus Hegland, Paul Leopardi
We examine sparse grid quadrature on weighted tensor products (WTP) of reproducing kernel Hilbert spaces on products of the unit sphere, in the case of worst case quadrature error…
On Tractability of Approximation for a Special Space of Functions
Markus Hegland, Greg W. Wasilkowski
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the pas…
Errors of regularisation under range inclusions using variable Hilbert scales
Markus Hegland, Bernd Hofmann
Based on the variable Hilbert scale interpolation inequality bounds for the error of regularisation methods are derived under range inclusions. In this context, new formulae for th…
Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities
Markus Hegland
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution.…
A Stabilized Mixed Finite Element Method for Thin Plate Splines Based on Biorthogonal Systems
Bishnu P. Lamichhane, Markus Hegland
The thin plate spline is a popular tool for the interpolation and smoothing of scattered data. In this paper we propose a novel stabilized mixed finite element method for the discr…
Dilational Hilbert Scales and Deconvolutional Sharpening
Markus Hegland, Robert S. Anderssen
Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms. Using a one parameter family of index functions based on the…