Schur Solver for Variational Propagator
Feature request:
When using the Variational Propagators, we use a Newton algorithm to solve the non-linear system. The Jacobian Matrix as form
$$\begin{pmatrix} A & B \ C & I \end{pmatrix}$$
Thus using a Schur complement method might allow for faster computation.
Furthermore, for the VariationalEntropyEvolve
and VariationalMagFieldEvolve
this system has the nice property that A-BC
is symmetric definite positive so that we can use an efficient pcg for even faster results.
Proposed solution:
Create another SchurSolver
(any idea for names to note mix it with the preexisting one is welcome) that allow to take advantage of this structure for faster solve.