Abstract A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian ix quantum-mechanic...

Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and -control of Markovian jump linear systems are considered. First, the L_ equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for existence of the maximal hermitian solution are derived in terms of the concept of mean sq...

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Suc...

We propose a class of regularized Hermitian and skew-Hermitian splitting methods for the solution of large, sparse linear systems in saddle-point form. These methods can be used as stationary iterative solvers or as preconditioners for Krylov subspace methods. We establish unconditional convergence of the stationary iterations and we examine the spectral properties of the corresponding precondi...

We show that the Euclidean condition number of any positive deenite Hankel matrix of order n 3 may be bounded from below by n?1 =(16n) with = exp(4Catalan==) 3:210, and that this bound may be improved at most by a factor 8n. Similar estimates are given for the class of real Vandermonde matrices, the class of row scaled real Vandermonde matrices, and the class of Krylov matrices with Hermitian a...

Abstract. It is well-known that non-periodic boundary conditions reduce considerably the overall accuracy of an approximating scheme. In previous papers the present authors have studied a fourth-order compact scheme for the one-dimensional biharmonic equation. It relies on Hermitian interpolation, using functional values and Hermitian derivatives on a three-point stencil. However, the fourth-or...

A theorem is proved on the structure of the group of isometries of an Hermitian map b : V × V → W , where V and W are vector spaces over a finite field of odd order. Also a Las Vegas polynomial-time algorithm is presented which, given an Hermitian map, finds generators for, and determines the structure of its isometry group. The algorithm can be adapted to construct the intersection of the memb...

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian positiondependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM – Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-l...

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form T (λ)v = 0 that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are generalizations of linear Hermitian eigenproblems Av=λBv. In this paper, we propose a Preconditioned Locally Minimal Residual (PLMR) method for efficiently computing interior...

A positive definite even Hermitian lattice is called even universal if it represents all even positive integers. We introduce a method to get all even universal binary Hermitian lattices over imaginary quadratic fields Q( √ −m) for all positive square-free integers m and we list optimal criterions on even universality of Hermitian lattices over Q( √ −m) which admits even universal binary Hermit...