Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.

Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and complex-valued energy eigenvalues and corresponding wave functions. Hamiltonian Hierarchy method is used in the calculations. PACS numbers: 03.65.-w; 03.65.Ge

We calculate genus one corrections to Hermitian one-matrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebro-geometrical considerations and generalizing it to the case of arbitrary potentials.

It is well known that the unitary evolution of a closed $M-$level quantum system can be generated by non-Hermitian Hamiltonian $H$ with real spectrum. Its Hermiticity restored via an amended inner-product metric $\Theta$. In Hermitian cases evaluation spectrum (i.e., bound-state energies) usually achieved diagonalization Hamiltonian. (or, more precisely, in $\Theta-$quasi-Hermitian) mechanics w...

The Hermitian and skew-Hermitian parts of a square matrix A are deened by H(A) (A + A)=2 and S(A) (A ? A)=2: We show that the function f(A) = (H(A ?1)) ?1 is convex with respect to the Loewner partial order on the cone of matrices with positive deenite Hermitian part. That is, for any matrices A and B with positive deenite Hermitian part ff(A) + f(B)g=2 ? f(fA + Bg=2) is positive semideenite: U...

The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain wall solution that admits a Killing spinor is shown to correspond to a cosmology that admits a pseudo-Killing spinor: whereas the Killing spinor obeys a Dirac-type equation with hermitian ‘mass’-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation...

We consider the problem of minimizing the spectral condition number of a positive definite matrix by completion: min{cond( [ A BH B X ] ) : [ A BH B X ] positive definite}, where A is an n × n Hermitian positive definite 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 solut...

Many problems in engineering and physics require the solution of a large sequence of linear systems. We can reduce the cost of solving subsequent systems in the sequence by recycling information from previous systems. We consider two di erent approaches. For several model problems, we demonstrate that we can reduce the iteration count required to solve a linear system by a factor of two. We con...

This paper looks at the iterative solution of complex, non-Hermitian systems of linear equations associated with a lattice QCD problem in particle physics. Let the n by n system of equations be Ax = b. We use a version of the GMRES method that deflates eigenvalues and can solve systems with multiple right-hand sides. We give examples that show deflating eigenvalues can make a significant improv...

Existence and uniqueness of the solution of time-harmonic electromagnetic boundary value problems is analyzed together with the convergence of Galerkin finite element approximations. Sufficient conditions based on the presence of different types of losses and on the properties of the hermitian symmetric parts of the effective dielectric permittivity and the effective magnetic permeability are p...