Related papers: Perturbation analysis for the periodic generalized…
A simple method for the calculation of higher orders of the logarithmic perturbation theory for bound states of the spherical anharmonic oscillator is developed. The structure of the perturbation series for energy eigenvalues of the sextic…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We present in this paper a family of generalized simultaneous perturbation-based gradient search (GSPGS) estimators that use noisy function measurements. The number of function measurements required by each estimator is guided by the…
The perturbation theory with a variational basis is constructed and analyzed.The generalized Gaussian effective potential is introduced and evaluated up to the second order for selfinteracting scalar fields in one and two spatial…
We perform a state-of-the-art study of the cosmological phase transitions of the real-scalar extended Standard Model. We carry out a broad scan of the parameter space of this model at next-to-next-to-leading order in powers of couplings. We…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
This paper considers the numerical solution of generalized Sylvester matrix equations, which arise in many scientific and engineering applications but remain challenging to solve efficiently, particularly when the coefficient matrices are…
We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps…
Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theorybased noniterative or approximate iterative treatments of triple excitations when applied to thedetermination of highly accurate potential energy…
Generalized Polynomial Chaos (gPC) expansions are well established for forward uncertainty propagation in many application areas. Although the associated computational effort may be reduced in comparison to Monte Carlo techniques, for…
This paper studies the influence of perturbations of conjugate priors in Bayesian inference. A perturbed prior is defined inside a larger family, local mixture models, and the effect on posterior inference is studied. The perturbation, in…
This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
The explicit semiclassical treatment of logarithmic perturbation theory for the nonrelativistic bound states problem is developed. Based upon $\hbar$-expansions and suitable quantization conditions a new procedure for deriving perturbation…
Some new rigorous perturbation bounds for the generalized Cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained, where the componentwise perturbation has the form of backward rounding error for…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
In this paper, we present perturbation analysis and randomized algorithms for the total least squares (TLS) problems. We derive the perturbation bound and check its sharpness by numerical experiments. Motivated by the recently popular…
Singular Spectrum Analysis and many other subspace-based methods of signal processing are implicitly relying on the assumption of close proximity of unperturbed and perturbed signal subspaces extracted by the Singular Value Decomposition of…