Investigating Computational Methods in Large Scale Data Processing

Abstract

The emergence of big data has revolutionized multiple fields, necessitating advanced numerical methods for the effective analysis of expansive and complex datasets. This paper presents a thorough review of numerical tech-niques applicable in big data scenarios, focusing on inverse problems, para-bolic and elliptic partial differential equations (PDEs), nonlinear systems, and operator-theoretic strategies. Highlighting recent advancements, such as the inverse Calderón problem and flux-saturated diffusion equations, we synthesize crucial methodologies while addressing computational challenges in high-dimensional contexts. The paper concludes with a critical evaluation of existing limitations and suggests future research avenues at the interface of numerical analysis and big data.