The Hybrid Mathematical Model for Interpolation and Prediction Based on FBGS Algorithm to Determine Optimal Weights with Real Data Application

Abdulrahman   Sh. Ahmed; Ghassan   E. Arif

doi:10.47831/mjpas.v4i3.541

Authors

Abdulrahman Sh. Ahmed Department of Mathematics, College of Education For Pure Sciences, Tikrit University
Ghassan E. Arif Department of Mathematics, College of Education For Pure Sciences, Tikrit University

DOI:

https://doi.org/10.47831/mjpas.v4i3.541

Keywords:

Mathematical interpolation, BFGS algorithm, Hybrid method, accuracy improvemen, MSE

Abstract

This study aims to improve prediction accuracy by applying a hybrid method based on
BFGS algorithm to select optimal weights that the best evaluate the solution weight at each
point. Newton and Lagrange's interpolation methods were used to construct the proposed
hybrid model structure. The performance of the three methods (the basic methods and
hybrid method) was evaluated through mean square error analysis. The results, applied to
real data representing the radon gas spread rate in Baghdad, showed that the hybrid method
clearly outperformed traditional methods, achieving a mean square error of 0.001501,
compared to 0.00876 for Newton method and 0.003216 for Lagrange method. This approach
contributes to improving prediction accuracy and reducing error by dynamically distributing
weights based on BFGS algorithm. This study a solid foundation for developing more
efficient models in various fields, such as temporal data forecasting and dynamic systems
analysis.