ABSTRACT
The relationship between the geometric sequence and the criterion for the applicability of the Shanks transform is independent of the framework from which the geometric sequence emerged. This is to say that the Shanks transform does not need to be restricted only to the problem of solving a system of inhomogeneous linear equations and can be linked directly to the Shanks sequence accelerations and signal processing. This chapter formulates a general problem using the concept of Schmidt relaxations within the realm of convergence acceleration of sequences and series. It shows how an induced convergence is an analytical continuation in the sense of enlarging the convergence radius of the original sequence.
