Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Faisal Kaleem
Pages: [241] - [249]
Received Date: June 11, 2010
Submitted by:
Lagrange interpolation is a classical technique of numerical analysis that is used to approximate functions by polynomials. On the other hand, Cauchy integral formula is one of the most important results in complex analysis. We will show in this article, how this famous formula can be applied to determine sufficient conditions for the convergence of interpolation polynomials to the desired function. Better sufficient conditions are known than the one give in this article, but they use advanced mathematical ideas. We will be using very elementary methods to arrive at results inferior to the best ones known, but nevertheless, very satisfactory in their beauty and simplicity.
Lagrange interpolation, convergence, Runge phenomenon.
