Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number cS, for invariant subspaces subject to structured perturbations. Several examples compare cS with the unstructured condition number. The examples include block ...

We present some Nekhoroshev stability results for nearly integrable, generalized Hamiltonian systems which can be odd dimensional and admit a distinct number of action and angle variables. Using a simultaneous approximation technique due to Lochak, Nekhoroshev stabilities are shown for various cases of quasi-convex generalized Hamiltonian systems along with concrete estimates on stability expon...

In this paper we consider the generalized algebraic Riccati equation (GARE) for a continuous-time descriptor system. Necessary and sucient conditions for the existence of stabilizing solutions of the GARE are derived based on the Hamiltonian matrix pencil approach. A parametrization of all stabilizing solutions is also provided. The main result has a potential applicability to a wide class of ...

We introduce and solve a generalized 1+1D Lorentzian gravity model in which a certain subclass of baby-universes is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle pointand path integral techniques we show that for β < 1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The ...

We propose a Preconditioned Locally Harmonic Residual (PLHR) method for computing several interior eigenpairs of a generalized Hermitian eigenvalue problem, without traditional spectral transformations, matrix factorizations, or inversions. PLHR is based on a short-term recurrence, easily extended to a block form, computing eigenpairs simultaneously. PLHR can take advantage of Hermitian positiv...

The trace variational identity is generalized to zero curvature equations associated with non-semi-simple Lie algebras or, equivalently, Lie algebras possessing degenerate Killing forms. An application of the resulting generalized variational identity to a class of semi-direct sums of Lie algebras in the AKNS case furnishes Hamiltonian and quasi-Hamiltonian structures of the associated integrab...

error group, 54Addelman and Kempthorne, 60adiabatic, 171adiabatic quantum computing, 171adjacency matrix, 94adjoint action, 76, 90amplification, 149annihilation operator, 134annihilator, 49, 50minimal, 50Arthur-Merlin games, 147average Hamiltonian, 44average Hamiltonian theory, 44 Bloch sphere, 33Bloch vector, 33BPP, 31BQP, 30 Carathéo...

Susan M. Mniszewski, CCS-3; Anders Niklasson, Ed Sanville, Marc J. Cawkwell, T-1 The performance of quantum-based molecular dynamics (MD) simulations using the LANL-developed code LATTE is limited by the time required to compute the density matrix at each time step. The density matrix has been computed historically via the diagonalization of the Hamiltonian matrix. We have investigated the perf...

A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$‎. ‎An $ntimes n$‎ ‎complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$)‎. ‎In this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexiv...