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.

Publications as TUM-IAS-Fellow

2015

  • A.P. Hinojosa, B. Harding, M. Hegland, and H.-J. Bungartz: SDC-Resilient Algorithms Using the Sparse Grid Combination Technique. SPPEXA Workshop 2016, 2015 mehr… BibTeX

2014

  • Khakhutskyy, Valeriy; Hegland, Markus: Parallel Fitting of Additive Models for Regression. In: Lecture Notes in Computer Science. Springer International Publishing, 2014 mehr… BibTeX Volltext ( DOI )
  • Khakhutskyy, Valeriy; Pflüger, Dirk: Alternating Direction Method of Multipliers for Hierarchical Basis Approximators. In: Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2014 mehr… BibTeX Volltext ( DOI )
  • Kowitz, Christoph; Hegland, Markus: An Opticom Method for Computing Eigenpairs. In: Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2014 mehr… BibTeX Volltext ( DOI )

2013

  • B. Harding and M. Hegland: A parallel fault tolerant combination technique. Proc. of the Int. Conf. on Parallel Computing, 2013 mehr… BibTeX
  • Harding, Brendan; Hegland, Markus: A robust combination technique. ANZIAM Journal 54, 2013, 394 mehr… BibTeX Volltext ( DOI )
  • Kowitz, Christoph; Hegland, Markus: The Sparse Grid Combination Technique for Computing Eigenvalues in Linear Gyrokinetics. Procedia Computer Science 18, 2013, 449-458 mehr… BibTeX Volltext ( DOI )
  • Larson, J.W.; Hegland, M.; Harding, B.; Roberts, S.; Stals, L.; Rendell, A.P.; Strazdins, P.; Ali, M.M.; Kowitz, C.; Nobes, R.; Southern, J.; Wilson, N.; Li, M.; Oishi, Y.: Fault-Tolerant Grid-Based Solvers: Combining Concepts from Sparse Grids and MapReduce. Procedia Computer Science 18, 2013, 130-139 mehr… BibTeX Volltext ( DOI )
  • Michael F. Barnsley, Markus Hegland, Peter Massopust: Numerics and Fractals. 2013 mehr… BibTeX
  • Wong, Matthias; Hegland, Markus: Maximum a posteriori density estimation and the sparse grid combination technique. ANZIAM Journal 54, 2013, 508 mehr… BibTeX Volltext ( DOI )

2012

  • Kowitz, Christoph; Pflüger, Dirk; Jenko, Frank; Hegland, Markus: The Combination Technique for the Initial Value Problem in Linear Gyrokinetics. In: Lecture Notes in Computational Science and Engineering. Springer Science + Business Media, 2012 mehr… BibTeX Volltext ( DOI )
  • Kowitz, Christoph; Pflüger, Dirk; Jenko, Frank; Hegland, Markus: The Combination Technique for the Initial Value Problem in Linear Gyrokinetics. In: Lecture Notes in Computational Science and Engineering. Springer Berlin Heidelberg, 2012 mehr… BibTeX Volltext ( DOI )

2011

  • Hegland, M.; Leopardi, P.C.: The rate of convergence of sparse grid quadrature on the torus. ANZIAM Journal 52, 2011 mehr… BibTeX
  • Hegland, Markus; Garcke, Jochen: On the numerical solution of the chemical master equation with sums of rank one tensors. ANZIAMJ 52, 2011, 628 mehr… BibTeX Volltext ( DOI )

2010

  • Griebel, Michael; Hegland, Markus: A Finite Element Method for Density Estimation with Gaussian Process Priors. SIAM Journal on Numerical Analysis 47 (6), 2010, 4759-4792 mehr… BibTeX Volltext ( DOI )