Generalization of Ramanujan Method of Approximating root of an equation
For mathematicians and numerical analysts, this work generalizes a classical method, but the contribution is incremental as it builds on existing techniques without demonstrating practical advantages over modern methods.
The paper generalizes Ramanujan's method for approximating the smallest root of an equation, providing an analytical proof of convergence and extending it to an iterative approach with arbitrary order of convergence.
We generalize Ramanujan method of approximating the smallest root of an equation which is found in Ramanujan Note books, Part-I. We provide simple analytical proof to study convergence of this method. Moreover, we study iterative approach of this method on approximating a root with arbitrary order of convergence.