The main application of SRA lies in finding the zeros of secular functions.
A divide-and-conquer algorithm to find the eigenvalues and eigenvectors for various kinds of matrices is well known in numerical analysis.
In a strict sense, SRA implies a specific interpolation using simple rational functions as a part of the divide-and-conquer algorithm.
The origin of the interpolation with rational functions can be found in the previous work done by Edmond Halley.
Similarly, we can derive a variation of Halley's formula based on a one-point second-order iterative method to solve
SRA strictly implies this one-point second-order interpolation by a simple rational function.