This chapter contains a review about nonlinear sequence transformations that have assumed in the past a key role in theoretical physics as powerful computational tools for the convergence acceleration of slowly convergent series as well as for the resummation of factorially divergent series. Some practical applications of a particular type of these transformations, the so-called Weniger transformation, to solve important problems within nonparaxial optics and catastrophe optics are illustrated.
Borghi, R. (2016). Computational Optics Through Sequence Transformations. In Progress in Optics (pp. 1-70). Elsevier [10.1016/bs.po.2016.02.001].