In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

Objective: By combining fractional calculus and duality theory, a novel fractional-order primal-dual model which is equivalent with the fractional ROF model is proposed. We theoretically analyze its structural similarity with the saddle-point optimization model. So the algorithms for solving the saddle-point problem can be used for solving the model. Methods: The primal-dual algorithm based on ...

We study Ε-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization of Ε-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between the Ε-Henig saddle point of the Lagrangian set-value...

Out-of-time-order correlators (OTOCs) have proven to be a useful tool for studying thermalization in quantum systems. In particular, the exponential growth of OTOCS, or scrambling, is sometimes taken as an indicator chaos systems, despite fact that saddle points integrable systems can also drive rapid OTOCs. By analyzing Dicke model and driven Bose-Hubbard dimer, we demonstrate OTOC by can, non...

We generalize the accelerated Hermitian and skew-Hermitian splitting (AHSS) iteration methods for large sparse saddle-point problems. These methods involve four iteration parameters whose special choices can recover the preconditioned HSS and accelerated HSS iteration methods. Also a new efficient case is introduced and we theoretically prove that this new method converges to the unique solutio...

We provide a general abstract theory for the solvability and Galerkin approximation of nonlinear twofold saddle point problems. In particular, a Strang error estimate containing the consistency terms arising from the approximation of the continuous operators involved is deduced. Then we apply these results to analyse a fully discrete Galerkin scheme for a twofold saddle point formulation of a n...

This paper provides a preconditioned iterative technique for the solution of saddle point problems. These problems typically arise in the numerical approximation of partial differential equations by Lagrange multiplier techniques and/or mixed methods. The saddle point problem is reformulated as a symmetric positive definite system, which is then solved by conjugate gradient iteration. Applicati...

The large-N saddle-point equations for the principal chiral models defined on a d − 1 dimensional simplex are derived from the external field problem for unitary integrals. The saddle point equation are studied analytically and numerically in many relevant instances, including d = 4 and d → ∞, with special attention to the critical domain, which is found to correspond to βc = 1/d for all d. Rel...