arXiv subjects
Publications and source records attributed to Ramesh Kumar Muthumalai.
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.
We show some definite integrals connecting to infinite series, studied in Ramanujan's paper, titled "On question 330 of Professor Sanjana". We present few recursive methods to evaluate these definite integrals in various cases and we generalize this, to evaluate simliar kind of integrals through infinite series.
We study few properties of square-free integers in certain equations. Using this property, we derive some infinite products in powers of square free numbers. Also, we present a method, to convert power series and trigonometric series to infinte products. Infinite products of few elementary trigonometric functions and factorials for large numbers are shown as examples.
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evanly or unevanly spaced data. Basic computer algorithms for new methods are given