The field of numerical approximation and scientific computation is moving towards the development of innovative methods for approximating special functions and performing scientific calculations. Researchers are exploring new approaches to transform complex functions into simpler forms, allowing for iterative refinement and increased accuracy.

A notable trend is the use of geometric methods and properties of similar triangles to perform error-free scientific calculations without the need for electronic calculators. Additionally, there is a focus on developing exponentially convergent algorithms for evaluating complex-valued error-like functions.

Some noteworthy papers include: The paper on numerical approximation of the Lambert W function, which introduces a unique method of quadratic approximation that works for both branches without restrictive initial assumptions. The paper on the evaluation of complex-valued error-like functions, which presents an exponentially convergent trapezoidal rule that achieves better accuracy and regular behavior of the relative error over vast regions of the complex plane.