Author(s)

Irina Viktorova, Sofya Alekseeva, Muhammed Kose

Mechanical Engineering Department, School of Mathematical and Statistical Sciences, Clemson University, Clemson, SC, USA.

Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L²-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.

Laplace Transform, Viscoelastic Composite, Norm Space, Inner Product Space, Least Squares Minimization, Optimal Parameter Estimation

Viktorova, I. , Alekseeva, S. and Kose, M. (2022) Mathematical Analysis of Two Approaches for Optimal Parameter Estimates to Modeling Time Dependent Properties of Viscoelastic Materials. Applied Mathematics, 13, 949-959. doi: 10.4236/am.2022.1312059.