Operator Newton Iterative Convergence for Time Dependent Density
By: J.W. Jerome
In a recent publication, the author has established the existence of a
unique weak solution of the initial/boundary value problem for a closed
quantum system modeled by time dependent density functional theory
(TDDFT). We describe a Newton iteration, based upon the technique used to
prove (unique) existence for the TDDFT model. We show that successive
approximation at the operator level, based upon the evolution operator, is
sufficient to obtain a `starting iterate' for Newton's method. We discuss
the so-called quadratic convergence associated with Newton's method. In
the process, we obtain a Kantorovich type theorem for TDDFT.
This paper was presented in preliminary form at IWCE-2015, at Purdue
University, and a version was posted on
IEEEXplore. We post here a newer version, with corrected typos.