The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the h̄-expansions and suitable quantization conditions a new procedure for deriving perturbation expansions is offered. Avoiding disadvantages of the standard approach, new handy recursion formulae with the same simple form both ...

The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the correspondig solution of the Bernoulli-Euler beam.The problem of convergence is related to a Singular Perturbation Problem. The main tool in solving this problem is a weak version of a lower bound for hyperbolic polynomials.

SUMMARY Perturbation bounds for Moore-Penrose inverses of rectangular matrices play a significant role in the perturbation analysis for linear least squares problems. In this note, we derive a sharp upper bound for Moore-Penrose inverses, which is better than a well known existing one [12].

The limit cycle bifurcations of a Z2 equivariant quintic planar Hamiltonian vector field under Z2 equivariant quintic perturbation is studied. We prove that the given system can have at least 27 limit cycles. This is an improved lower bound on the possible number of limit cycles that can bifurcate from a quintic planar Hamiltonian system under quintic perturbation.

We present a new PAC-Bayes generalization bound for structured prediction that is applicable to perturbation-based probabilistic models. Our analysis explores the relationship between perturbation-based modeling and the PAC-Bayes framework, and connects to recently introduced generalization bounds for structured prediction. We obtain the first PAC-Bayes bounds that guarantee better generalizati...

In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition numbers of eigenvalues and the pseudospectral growth rate. We obtain that if a simple eigenvalue of a matrix polynomial is ill-conditioned in some respects, th...

A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value above a specified level. Such problems can be addressed using perturbation analysis. In this paper, we propose a perturbation bound for the smallest singular ...

In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition numbers of eigenvalues and the pseudospectral growth rate. We obtain that if a simple eigenvalue of a matrix polynomial is ill-conditioned in some respects, th...

• A spectral norm bound for reconstruction error for the basic low-rank approximation random sampling algorithm. • A discussion of how similar bounds can be obtained with a variety of random projection algorithms. • A discussion of possible ways to improve the basic additive error bounds. • An iterative algorithm that leads to additive error with much smaller additive scale. This will involve u...

In this paper we consider the upper bound for the sine of the greatest canonical angle between the original invariant subspace and its perturbation. We present our recent results which generalize some of the results from the relative perturbation theory of indefinite Hermitian matrices.