Applied Mathematics in the Design of Efficient Algorithms for Big Data Analytics

This study explores the application of applied mathematics to big data analytics, exploring optimization through algorithms for effective processing in a computational efficiency with assurance of accuracy on any related domain. This paper further suggests and examines four types of algorithms, which include optimization-based algorithms, machine learning models, digital twin frameworks, and methods for the protection of privacy. The experimental results show that the optimization algorithm has reduced the processing time by 25%. On the other hand, the machine learning models enhanced the models predictive capabilities by 15 percent compared to conventional techniques. The major achievements of the proposed framework include; the Digital Twin framework enhanced the processing efficiency by 20% of the real time data simulation of manufacturing, and the Privacy Protection algorithm enhanced non-disclosure of data by 30%. Comparison with related work was also made to measure the performance of these algorithms and it was witnessed that the introduced techniques offer better accuracy, less time required and better scalability than existing models. The results will demonstrate the critical role of applied mathematics in addressing big data management and analytics issues across the sectors such as health care, manufacturing, and energy. Building on this previous work, it has set the groundwork for subsequent research to engage in the further development of more efficient and safer algorithms for the analysis of big data in real time, with strict regard to data privacy.