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Table 1 Overview of the regularization tuning methods considered. We have indicated with a sign for each method, (i) which data/information is required (residual vector, estimated kinetic model parameters or the Jacobian of the residual vector), and (ii) whether the regularization method utilizes further tuning parameters, an estimate of the measurement noise level or a limit for the maximal/minimal regularization parameter. Finally, the last three columns indicate if a computationally expensive procedure is involved, which can be an issue for large scale problems. SVD denotes singular value decomposition

From: Robust and efficient parameter estimation in dynamic models of biological systems

Regularization method Computation involves Further required inputs Involved computation
Method Short ID Refs Residuals Estimated Jacobian Tuning Meas. error α max/α min Matrix SVD Trace
     parameters   parameter estimate   inverse   
Discrepancy principle DP [113] - - - - - -
Modified DP MDP [114] - - - -
Transformed DP TDP [115] - - - -
Monotone Error Rule MER [116] - - -
Balancing Principle BP [117] - - - -
Hardened Balancing HBP [118] - - - - - -
Quasi optimality QO [80] - - - - - - -
L–curve method (curvature) LCC [105] - - - - - -
L–curve method (Reginska) LCR [119] - - - - - -
Extrapolated Error Rule EER [120] - - - - - - -
Residual Method RM [121] - - - -
Generalized Cross-validation GCV [122] - - - - -
GCV (Golub) GCVG [107] - - - - -
Robust GCV RGCV [108] - - - -
Strong RGCV SRGCV [109] - - - -