Matrix Science Mathematic (MSMK)

We aimed to develop a conjugate gradient method by reformulating parameters so that iterative optimization techniques perform more effectively. Instead of using a set of basic conjugate gradient formulas, the methodology introduces a new parameter that produces better convergence. The method is applied in Fortran to test how many iterations and how many evaluations of the function are needed, as listed in table 1. The behavior of convergence and the results used for comparison are created with Matplotlib on Python and Ggplot2 on R programming for the chart. We like to compare our method to the proven LS (Liu-Storey) method when checking how effective our proposed method is. We found that the technique provides better results with lower iteration numbers and better convergence speeds for many test cases, proving it can challenge conventional methods in optimizing problems without constraints.