My research interests are in the areas of inverse problems, spline smoothing and numerical analysis. In particular, I am interested in the methodology of regularization methods for solving ill-posed problems and the effective choice of the regularization parameter. The framework and analysis may be either deterministic or stochastic. I am also interested in the smoothing of noisy data by splines and the selection of the smoothing parameter.

Lukas, M., de Hoog, F., Anderssen, R., (2016), Practical use of robust GCV and modified GCVfor spline smoothing, Computational Statistics, 31, 1, pages 269 - 289. Lukas, M., (2014), Performance criteria and discrimination of extreme undersmoothing in nonparametric regression, Journal of Statistical Planning and Inference, 153, , pages 56 - 74. Lukas, M., De Hoog, F., Anderssen, R., (2012), Performance of Robust GCV and Modified GCV for Spline Smoothing, Scandinavian Journal of Statistics: theory and applications, 39, 1, pages 97 - 115. De Hoog, F., Anderssen, R., Lukas, M., (2011), Differentiation of matrix functionals using triangular factorization, Mathematics of Computation, 80, 275, pages 1585 - 1600. Bauer, F., Lukas, M., (2011), Comparing parameter choice methods for regularization of ill-posed problems, Mathematics and Computers in Simulation, 81, 9, pages 1795 - 1841. Lukas, M., de Hoog, F., Anderssen, R., (2010), Efficient algorithms for robust generalized cross-validation splinesmoothing, Journal of Computational and Applied Mathematics, 235, 1, pages 102 - 107. Lukas, M., (2010), Robust GCV choice of the regularization parameter for correlated data, Journal of Integral Equations and Applications, 22, 3, pages 519 - 547. Lukas, M., (2008), Strong robust generalized cross-validation for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 24, 3, pages 1 - 16. Lukas, M., (2006), Robust generalized cross-validation for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 22, , pages 1883 - 1902. Lukas, M., Shi, M., (2006), Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations, Computational Statistics & Data Analysis, 51, , pages 1213 - 1231. Shi, M., Lukas, M., (2005), Sensitivity analysis of constrained linear L1 regression: perturbations to response and predictor variables, Computational Statistics & Data Analysis, 48, , pages 779 - 802. Shi, M., Lukas, M., (2002), An L1 estimation algorithm with degeneracy and linear constraints, Computational Statistics & Data Analysis, 39, , pages 35 - 55. Abo-Hashema, K., Cake, M., Lukas, M., Knudsen, J., (2001), The interaction of acyl-CoA with acyl-CoA binding protein and carnitine palmitoyltransferase I, International Journal of Biochemistry & Cell Biology, 33, , pages 807 - 815. Abo-Hashema, K., Cake, M., Lukas, M., Knudsen, J., (1999), Evaluation of the Affinity and Turnover Number of Both Hepatic Mitochondrial and Microsomal Carnitine Acyltransferases: Relevance to Intracellular Partitioning of Acyl-CoAs, Biochemistry, 38, 48, pages 15840 - 15847. Lukas, M., (1998), Asymptotic behaviour of the minimum bound method for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 14, , pages 149 - 159. Lukas, M., (1998), Comparisons of parameter choice methods for regularization with discrete noisy data, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 14, , pages 161 - 184.