Markus Hegland

Short CV

Markus Hegland is a member of the Computational Mathematics Group at the Institute of Advanced Studies of the Australian National University (ANU). Since 2012 he is Head of the ANU Centre for Mathematics and its Applications (CMA) and Associate Director Research of Mathematics. He received his doctoral degree at the ETH Zurich in 1988. Afterwards and until 1991, he worked as a researcher and support staff under Prof. Martin Gutknecht at the Interdisciplinary Project Centre for Supercomputing (IPS) of the ETH Zurich. In 1992, Prof. Hegland joined an HPC group at the Australian National University (ANU) where he worked on algorithms for Fujitsu’s VPP and AP series. He also continued research on the solution of ill-posed problems. In the late 1990s, he established the first data mining course at the ANU and acted as leader of a data mining group. In recent years, Prof. Hegland has been a chief investigator in the ARC (Australian Research Council) Centre of Excellence in Bioinformatics. Currently he is involved in collaborative ARC funded research with Fujitsu on fault tolerance and HPC.

Research Interests

Markus Hegland's research is in numerical analysis and he is in particular interested in the challenges posed by high dimensional problems and by ill-posed problems. He has introduced and analysed "OPTICOM", a stable variant of the sparse grid combination technique for the solution of multidimensional problems, and has established the convergence theory for regularisation based on "Variable Hilbert Scales". In the 1990s Markus Hegland has developed and implemented several HPC algorithms for FFTs, discrete wavelet transforms and for the solution of banded linear systems of equations. More recently, he has worked on applications in data mining, systems biology and spectral enhancement.

Selected Publications

• Hegland, Markus; Burden, Conrad; Santoso, Lucia; MacNamara, Shev; Booth, Hilary: A solver for the stochastic master equation applied to gene regulatory networks. Journal of Computational and Applied Mathematics 205 (2), 2007, 708-724.

• Hegland, Markus; Garcke, Jochen; Challis, Vivien: The combination technique and some generalisations. Linear Algebra and its Applications 420 (2-3), 2007, 249-275.

• Hegland, M.; Nielsen, O.M.; Shen, Z.: Multidimensional smoothing using hyperbolic interpolatory wavelets. Electronic Transactions on Numerical Analysis 17, 2004, 168-180.

• Roberts, Stephen; Hegland, Markus; Altas, Irfan: Approximation of a Thin Plate Spline Smoother Using Continuous Piecewise Polynomial Functions. SIAM Journal on Numerical Analysis 41 (1), 2003, 208-234.

• Nielsen, O.M.; Hegeland, M.: PARALLEL PERFORMANCE OF FAST WAVELET TRANSFORMS. Int. J. High Speed Comp. 11 (01), 2000, 55-74.

• Anderssen, Robert S.; Hegland, Markus: For numerical differentiation, dimensionality can be a blessing! Mathematics of Computation 68 (227), 1999, 1121-1142.

• Hegland, Markus: Real and complex fast Fourier transforms on the Fujitsu VPP 500. Parallel Computing 22 (4), 1996, 539-553.

• Hegland, Markus: An Optimal Order Regularization Method which Does Not Use Additional Smoothness Assumptions. SIAM Journal on Numerical Analysis 29 (5), 1992, 1446-1461.

• Hegland, Markus: On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization. Numer. Math. 59 (1), 1991, 453-472.