Modified Least Squares Method and a Review of Its Applications in Machine Learning and Fractional Differential/Integral Equations

Abstract

Abstract. The least squares method provides the best-fit curve by minimizing the total squared error. In this work, we propose a modified least squares method based on fractional orthogonal polynomials that belong to the space Mnλ:=span{1,xλ,x2λ,…,xnλ}, λ∈(0,2]. Numerical experiments demonstrate how to solve different problems using the modified least squares method. Moreover, the results show the advantage of the modified least squares method compared to the classical least squares method. Furthermore, we discuss the various applications of the modified least squares method in fields such as fractional differential/integral equations and machine learning.