Stochastic Influence on Levenberg-Marquardt Method for Nonlinear Least Squares Problems - Christopher, Gerend; Naiborhu, Janson (IndoMS, 2026)
In this digital era, a lot of data can be collected to be extracted and used for decision making through mathematical models in solving cases in certain domains. This paper will focus on solving nonlinear least squares problems in building an optimal model, namely one that has good accuracy and is efficient. In practice, the model is built using numerical methods. The main objective of this study is to investigate the effect of stochasticity in numerical methods that utilize gradients, namely Levenberg-Marquardt, on accuracy and computational efficiency. In addition, several numerical results from several variants of Stochastic Levenberg-Marquardt sampling and data taken in clusters with K-Means will be compared. The results of this paper are Stochastic Levenberg-Marquardt with 100, 200, 300, 400, and 500 data sample sizes outperformed classical Levenberg-Marquardt since they have very low relative errors to Levenberg-Marquardt and are faster in computational time than Levenberg-Marquardt. Therefore, when solving nonlinear least squares problems with large data sets, the Levenberg-Marquardt method requires only a small number of samples, which suggests that using the Stochastic Levenberg-Marquardt approach is advantageous.