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...

A non-Hermitian PφTφ-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians Hr, Hθ, and Hφ play essential roles and offer some ”user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a PφTφ-symmetrized Hφ, we have shown that the conventional relativistic energy eigenvalues are recoverable. We h...

We consider the problem of minimizing the spectral condition number of a positive deenite matrix by completion: minfcond(positive deeniteg; where A is an n n Hermitian positive deenite matrix, B a p n matrix and X is a free p p Hermitian matrix. We reduce this problem to an optimization problem for a convex function in one variable. Using the minimal solution of this problem we characterize the...

We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algori...

In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such system where is an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, Hamiltonian pseudo-Hermitian/PT-symmetric, as strength of coupling environment increased spectrum in fixed symmetry sector changes ...

We discuss iterative methods for the solution of the linear system Ax = b, which are based on a single splitting or a multisplitting of A. In order to compare diierent methods , it is common to compare the spectral radius of the iterative matrix. For M{matrices A and weak regular splittings there exist well-known comparison theorems. Here, we give a comparison theorem for splittings of Hermitia...

Despite the didactic importance of a free particle in quantum mechanics, its coherent state analysis has long been untouched. It is only recently that it has been noticed and studied in the semiclassical domain. While the previously known solutions, reported by Bagrov et al. for a free particle, are described using the linear non-Hermitian invariant operator, we show in this work that the gener...

1 Hermitian eigenvalue problem For any n × n Hermitian matrix A, let λA = (λ1 ≥ · · · ≥ λn) be its set of eigenvalues written in descending order. (Recall that all the eigenvalues of a Hermitian matrix are real.) We recall the following classical problem. Problem 1. (The Hermitian eigenvalue problem) Given two n-tuples of nonincreasing real numbers: λ = (λ1 ≥ · · · ≥ λn) and μ = (μ1 ≥ · · · ≥ μ...