  Relying on fixed point techniques, Mahey, Oualibouch and Tao introduced the
scaled proximal decomposition on the graph of a maximal monotone operator
(SPDG) algorithm and analyzed its performance on inclusions for strongly
monotone and Lipschitz continuous operators. The SPDG algorithm generalizes the
Spingarn's partial inverse method by allowing scaling factors, a key strategy
to speed up the convergence of numerical algorithms. In this note, we show that
the SPDG algorithm can alternatively be analyzed by means of the original
Spingarn's partial inverse framework, tracing back to the 1983 Spingarn's
paper. We simply show that under the assumptions considered by Mahey,
Oualibouch and Tao, the Spingarn's partial inverse of the underlying maximal
monotone operator is strongly monotone, which allows one to employ recent
results on the convergence and iteration-complexity of proximal point type
methods for strongly monotone operators. By doing this, we additionally obtain
a potentially faster convergence for the SPDG algorithm and a more accurate
upper bound on the number of iterations needed to achieve prescribed
tolerances, specially on ill-conditioned problems.
