Let us now study the stability and the convergence of the algorithm of the deterministic gradient.
By taking the recursive expressions of the coefficient vector and by translation:
The following expressions
enable us to write: αK+1 = (Id − 2μR)αK Id: identity matrix.
By writing R in the form
and by premultiplying αK+1 by Q−1, we obtain:
Thus, the algorithm is stable and convergent if
Thus, if and only if
Thus, if and only if:
In addition, we ...