Vedic Techniques of Approximation: A Computational and Iterative Perspective for Modern Scientific Applications

Abstract

The paper “Vedic Techniques of Approximation: Iterative Methods, Infinite Series, and Their Relevance to Modern Computation” presents a reinterpretation of approximation methods developed in classical Indian mathematics within a contemporary computational framework. Selected techniques, including Aryabhata’s rational estimation of π, complement-based arithmetic procedures, and infinite series formulated by mathematicians of the Kerala school, are examined as structured processes of iterative refinement and controlled numerical approximation. Rather than viewing these contributions solely from a historical perspective, the study analyzes their mathematical structure using modern concepts such as recursion, convergence, and algorithmic approximation. The discussion further explores the conceptual relevance of these methods to present-day computational practices. The work demonstrates that classical approximation strategies embody principles consistent with modern algorithmic thinking and continue to offer meaningful insights for efficient computational methodologies.