  In this work, we propose and study a preconditioned framework with a graphic
Ginzburg-Landau functional for image segmentation and data clustering by
parallel computing. Solving nonlocal models is usually challenging due to the
huge computation burden. For the nonconvex and nonlocal variational functional,
we propose several damped Jacobi and generalized Richardson preconditioners for
the large-scale linear systems within a difference of convex functions
algorithms framework. They are efficient for parallel computing with GPU and
can leverage the computational cost. Our framework also provides flexible step
sizes with a global convergence guarantee. Numerical experiments show the
proposed algorithms are very competitive compared to the singular value
decomposition based spectral method.

Numerical Analysis;Numerical Analysis;Optimization and Control