On improving convergence of alternating series

Abstract

The root α of the equation can be determined by using the iterative formula provided that x ₀is a good starting approximation to α and It is noted here that there are advantages in using the formula and, where λ is suitably chosen, this formula is equivalent to Aitken's; δ²extrapolation formula. The iterative technique is found to be successful in speeding up the convergence of alternating series and has also been applied to finding zeros of the Riemann Zeta Function.

Keywords:

• Iterative methods
• Aitken's δ²-extrapolation formula
• alternating series
• Riemann Zeta Function

C.R. Categories:

• 5.12
• 5.15