Core Concepts
Efficient convergence acceleration using enhanced Neville algorithm.
Abstract
The content discusses the application of the enhanced Neville algorithm for convergence acceleration in slowly convergent series. It introduces a matrix-based formulation to estimate the limit and subleading terms efficiently. Comparison with other methods like Aitken's ∆2 process and Wynn's epsilon algorithm is made, showing superior performance. Numerical examples are provided for model series and Bethe logarithms calculations. The results showcase high accuracy and efficiency in estimating convergence rates.
Stats
Bethe logarithm for hydrogen ground state: ln k0(1S) = 2.98412 85557 65497 61075 97770 90013 79796 99751 80566 17002 (100 decimal digits)
Coefficients: c1 = -1, c2 = 0.81830, c3 = -0.80328, c4 = 0.98145 (verified to about 100 digits)