Technische Universität München

10 selected publications:

Markus Hegland. On the parallel solution of tridiagonal systems by wrap-around partitioning and incomplete LU factorization. Numer. Math., 59(5):453-472, 1991.

New stable and parallel solver. Has been extended and applied many times since. A variant of this algorithm for banded systems is included in Scalapack.

http://dx.doi.org/10.1007/BF01385791

Markus Hegland. An optimal order regularization method which does not use additional smoothness assumptions.

SIAM J. Numer. Anal., 29(5):1446-1461, 1992.

Established "Variable Hilbert Scales" and substantial extension of the theory of the solution of operator equations with compact operators.

http://dx.doi.org/10.1137/0729083

Markus Hegland. Real and complex fast Fourier transforms on the Fujitsu VPP 500. Parallel Computing, 22:539-553, 1996. New in-place and self-sorting FFT algorithms based on systematic framework (like BLAS in linear algebra). In Fujitsu's highperformance computing library and component in a patent.

http://dx.doi.org/10.1016/0167-8191(96)00015-4

Robert S. Anderssen and Markus Hegland.

For numerical differentiation, dimensionality can be a blessing!

Math. Comp., 68(227):1121-1141, 1999.

Contrary to intuition, differentiation benefits from high-dimensionality. Exemplified with a method originally suggested by the authors and F. deHoog.

URL: http://dx.doi.org/10.1090/S0025-5718-99-01033-9

Ole Moeller Nielsen and Markus Hegland.

Parallel performance of fast wavelet transform.

International Journal of High Speed Computing, 11:55-73, 2000. One of the first vector-parallel fast discrete wavelet transforms.

Stephen Roberts, Markus Hegland and Irfan Altas.

Approximation of a thin plate spline smoother using continuous piecewise polynomial functions.

SIAM J. Numer. Anal., 41(1):208-234 (electronic), 2003.

A comprehensive error analysis of a new approach for smoothing which scales with the amount of data.

http://dx.doi.org/10.1137/S0036142901383296

Markus Hegland, Ole M. Nielsen and Zuowei Shen.

Multidimensional smoothing using hyperbolic interpolatory

wavelets.

Electron. Trans. Numer. Anal., 17:168-180 (electronic), 2004.

One of the first data mining applications of sparse grids. Was developed simultaneously and independently of Griebel and Garcke but publication appeared later.

http://etna.math.kent.edu/vol.17.2004/pp168-180.dir/pp168-180.pdf

Markus Hegland, Jochen Garcke, and Vivien Challis.

The combination technique and some generalisations.

Linear Algebra Appl., 420(2-3):249-275, 2007.

Explains reasons for the breakdown of the sparse grid combination technique and analyses the cure (the Opticom method proposed by the applicant).

http://dx.doi.org/10.1016/j.laa.2006.07.014

Markus Hegland, Conrad Burden, Lucia Santoso, Shev MacNamara, and Hilary Booth.

A solver for the stochastic master equation applied to gene regulatory networks.

J. Comput. Appl. Math., 205(2):708-724, 2007.

New solution technique for chemical master equation for higher dimensions. First sparse grid method applied to this problem.

http://dx.doi.org/10.1016/j.cam.2006.02.053

Michael Griebel and Markus Hegland.

A finite element method for density estimation with Gaussian process priors.

SIAM J. Numer. Anal., 47(6):4759-4792, 2010.

Provides the numerical theory and the stochastic derivation of a density estimator.

http://dx.doi.org/10.1137/080736478

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.