  We introduce a new regularization of the Redfield equation based on a
replacement of the Kossakowski matrix with its closest positive semidefinite
neighbor. Unlike most of the existing approaches, this procedure is capable of
retaining the time dependence of the Kossakowski matrix, leading to a
completely positive divisible quantum process. Using the dynamics of an
exactly-solvable three-level open system as a reference, we show that our
approach performs better during the transient evolution, if compared to other
approaches like the partial secular master equation or the universal Lindblad
equation. To make the comparison between different regularization schemes
independent from the initial states, we introduce a new quantitative approach
based on the Choi-Jamiolkowski isomorphism.
