We present the first order error bound for the Lyapunov equation AX +XA∗ = −GG∗, where A is perturbed to A+ δA. We use the structure of the solution of the Lyapunov equation X = m ∑ k=1 WkW ∗ k , where Wk is the k-th matrix obtained by the Low Rank Cholesky Factor ADI (LRCF-ADI) algorithm using the set of ADI parameters equal to exact eigenvalues of A, that is with ADI parameters {p1, . . . , p...

The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon ¯ h-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions for the one-dimensional anharmonic oscillator is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same ...

We calculate the critical value of the hopping parameter, κc, in Lattice QCD with Wilson fermions, to two loops in perturbation theory. This quantity is an additive renormalization; as such, it is characterized not only by the standard caveats regarding the asymptotic nature of perturbative results, but also by a linear divergence in the lattice spacing. Consequently, our calculation tests rath...

We investigate the mesonic light-front bound-state equations of the ’t Hooft and Schwinger model in the two-particle, i.e. valence sector, for small fermion mass. We perform a high precision determination of the mass and light-cone wave function of the lowest lying meson by combining fermion mass perturbation theory with a variational approach. All calculations are done entirely in the fermioni...

We analyse the data for the proton structure function F 2 over the entire Q 2 domain, including especially low Q 2 , in terms of perturbative and non-perturbative QCD contributions. The small distance configurations are given by perturbative QCD, while the large distance contributions are given by the vector dominance model and, for the higher mass qq states, by the additive quark approach. The...

Let N0 and Z denote the nonnegative integers and integers, respectively, and let |A| denote the cardinality of the set A. Let A be a set of integers, and consider the sumset 2A = {a + a : a, a ∈ A}. Let S be a set of integers. The set A is a basis of order 2 for S if S ⊆ 2A. The set A is called a basis of order 2 for n if the sumset 2A contains the first n nonnegative integers, that is, if A is...

Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper is less restrictive on the norm of the perturbation and provides a potentially tighter bound compared to Stewart’s classical result. Moreover, we provide norm estimates for the remainder terms in well-known perturbation expansions for invariant subspaces, eig...

We give a sharp estimate for the eigenvectors of a positive deenite Hermitian matrix under a oating-point perturbation. The proof is elementary. Recently there have been a number of papers on eigenvector perturbation bounds that involve a perturbation of the matrix which is small in some relative sense, including the typical rounding errors in matrix elements ((1], 2], 10], 8], 4], 5]). The pro...

An injective coloring of a graph is a vertex labeling such that two vertices sharing a common neighbor get different labels. In this work we introduce and study what we call additive colorings. An injective coloring c : V (G) → Z of a graph G is an additive coloring if for every uv, vw in E(G), c(u)+ c(w) = 2c(v). The smallest integer k such that an injective (resp. additive) coloring of a give...

Control of a class of uncertain nonlinear systems, which estimates unavailable state variables, is considered. A new approach for robust tracking control problem of satellite for large rotational maneuvers is presented in this paper. The features of this approach include a strong algorithm to estimate attitude, based on discrete extended Kalman filter combined with a continuous extended Kalman ...