Conjugate Gradient Methods in Fitting Precipitation of Rainfall Data in Malaysia

Conjugate gradient method (CGM) is one of the most efficient numerical methods for solving unconstrained optimization problems. It is also known as an iterative method with simple formulation. The classical CGM has always been an interest to the current researchers in improving the formulation which are categorized into three-term (TTCGM), spectral (SCGM), hybrid and scaled CGM. Although there are many variations of the CGM available, choosing the most efficient and effective one for a particular problem can be a time-consuming process. In this study, spectral Hestenes-Stiefel (sHS) CGM with the greatest NOI and central processing time per unit (CPU time) is selected as the efficient method to be applied to the real-life problems in regression analysis. A data set of rainfall precipitation in Malaysia from year 2009 until 2019 is collected for data fitting purpose. The data set is transformed into a test function also defined as objective function. The approximate functions are generated from CG, Least Square, Trendline method for the relative error purpose. The estimation data for the year 2020 can be predicted using the approximate functions. The calculation of relative error of the linear and quadratic model for each method is calculated based on the estimation data for the year 2020 and its actual data. The numerical results show that the sHS CGM is a suitable and good alternative to solve the Least Square models.