Rate My Professor Mark Lukas

Dr. Mark Lukas is an Adjunct Senior Lecturer in the School of Mathematics, Statistics, Chemistry and Physics at Murdoch University. His career at Murdoch University spans several decades, during which he has focused on numerical analysis and applied mathematics, specializing in regularization methods for solving ill-posed inverse problems. These include Tikhonov regularization, robust generalized cross-validation (GCV) for parameter choice, spline smoothing techniques, and L1 estimation algorithms under linear constraints. He completed his PhD with a thesis entitled "Regularization of linear operator equations."

Dr. Lukas has authored numerous peer-reviewed publications in prestigious journals such as Inverse Problems, Journal of Computational and Applied Mathematics, Scandinavian Journal of Statistics, and Mathematics of Computation. Key works include "Robust generalized cross-validation for choosing the regularization parameter" (Inverse Problems, 2006), "Comparisons of parameter choice methods for regularization with discrete noisy data" (Inverse Problems, 1998), "Efficient algorithms for robust generalized cross-validation spline smoothing" (Journal of Computational and Applied Mathematics, 2010), "Performance of Robust GCV and Modified GCV for Spline Smoothing" (Scandinavian Journal of Statistics, 2012), "Practical use of robust GCV and modified GCV for spline smoothing" (Statistics and Computing, 2015), "Robust GCV choice of the regularization parameter for correlated data" (Journal of Integral Equations and Applications, 2010), "Strong robust generalized cross-validation for choosing the regularization parameter" (Inverse Problems, 2008), "Sensitivity analysis of constrained linear L1 regression: perturbations to response and predictor variables" (Computational Statistics & Data Analysis, 2005), "An L1 estimation algorithm with degeneracy and linear constraints" (Computational Statistics & Data Analysis, 2002), and "Asymptotic behaviour of the minimum bound method for choosing the regularization parameter" (Inverse Problems, 1998). Additionally, he has contributed to "Robust generalized cross-validation formulas for spline smoothing" (Mathematics of Computation, 2011). Dr. Lukas has also served as co-supervisor for PhD theses at Murdoch University, including "A dynamical study of saline plumes in desalination outfalls" by S.M. Shraida (2022) and "Selective withdrawal and the effect of surface tension on selective withdrawal flows" by H. Nguyen (2025). His research addresses practical challenges in handling noisy and correlated data in regularization processes.