OPTIMIZING MATHEMATICAL ALGORITHMS FOR REALTIME COMPUTATIONAL APPLICATIONS

The increasing demand for rapid data processing and intelligent decision-making has significantly enhanced the importance of predictive analytics in modern industrial and computational systems. Real-time applications such as robotics, healthcare monitoring, financial trading, and smart manufacturing require efficient mathematical algorithms capable of handling large volumes of dynamic data with minimal latency. This review paper focuses on optimizing mathematical algorithms for real-time computational applications, emphasizing their role in improving system performance, computational efficiency, and scalability. The study analyzes various mathematical modelling and optimization techniques, including complexity reduction methods, numerical optimization, heuristic and metaheuristic approaches, and parallel and distributed computing. Additionally, advanced computational strategies such as machine learning-based optimization, approximation algorithms, streaming data processing, and hardware acceleration using GPUs and FPGAs are explored. The findings highlight that optimized algorithms significantly enhance processing speed, reduce computational overhead, and enable accurate real-time predictions across multiple domains. Furthermore, the integration of mathematical modelling with modern computational technologies improves system responsiveness and decision-making capabilities. In conclusion, the adoption of optimized mathematical algorithms, combined with emerging Industry 4.0 technologies such as artificial intelligence and edge computing, plays a crucial role in devel oping efficient, scalable, and intelligent real-time computational systems.