Ramesh Kumar Muthumalai
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
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.
Ramesh kumar muthumalai
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
Ramesh kumar Muthumalai
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of accuracy for evanly and unevanly spaced data. First, we study the new interpolation formula which generalizes both Newton's and Lagrange's interpolation formula with the new divided difference table for unevanly spaced points and using this; we derive other interpolation formulas, in terms of differences for evanly spaced data. Second, we study two new different methods of numerical differentiation for both evanly and unevanly spaced points without differentiating the interpolating polynomials or the use of operators. Third, we derive new numerical integration formulas using new differentiation formulas and Taylor formula for both evanly and unevanly spaced data. Basic computer algorithms for few new formulas are given. In Comparison to former polynomial interpolation, numerical differentiation and numerical integration formuals, these new formulas have some featured advantages for approximating functional values, numerical derivatives of higher order and approximate integral values for evanly and unevanly spaced data.