Stochastic Influence on Gradient Numerical Methods for Nonlinear Least Squares Problems
Gerend Christopher (1), Janson Naiborhu (1)

(1) Department of Mathematics, Institut Teknologi Bandung, Jl Ganesa 10 Bandung 40132, Indonesia

Abstract

The development of knowledge in the fields of mathematics, science and technology has brought humans into the information and digital era. This change leads to changes in the amount of data collected to be extracted and used for various purposes, one of them through mathematical models. There are many forms of mathematical models that are built to solve cases in certain domains. In this paper, the focus will be on solving nonlinear least squares problems. In building a model, the model that wanted to be built is an optimal model, that is, it has good accuracy and is efficient. In practice, models are built using numerical methods. The main purpose of this research is to investigate the influence of stochastic in numerical methods that utilize gradients, namely Levenberg-Marquardt, on accuracy and computational efficiency. Apart from that, several numerical results from several Stochastic Levenberg-Marquardt variants sampling and data taken in clusters will be compared. The result of this paper is Stochastic Levenberg-Marquardt with 100, 200, 300, and 400 are superior for having a very low relative error to Levenberg-Marquardt and faster than Levenberg-Marquardt in computational time

Keywords: Nonlinear Least Squares, Stochastic Levenberg-Marquardt, Cluster, Accuracy, Computational Efficiency

Topic: Others