series acceleration

Series acceleration is a mathematical technique used to improve the convergence of a series, making its sum easier to approximate more quickly. When a series converges slowly, it takes many terms to get an accurate result. By applying acceleration methods, such as Aitken’s delta-squared process or Shanks transformation, we transform the original series into a new one that approaches the sum faster. This approach is useful in computational mathematics and physics to efficiently evaluate series, especially those that converge very slowly or are difficult to sum directly.