Related papers: Perturbation analysis for the periodic generalized…
In this paper, we concentrate on the backward error and condition number of the indefinite least squares problem. For the normwise backward error of the indefinite least square problem, we adopt the linearization method to derive the tight…
The condition number of a linear function of the indefinite least squares solution is called the partial condition number for the indefinite least squares problem. In this paper, based on a new and very general condition number which can be…
In this paper, the normwise condition number of a linear function of the equality constrained linear least squares solution called the partial condition number is considered. Its expression and closed formulae are first presented when the…
In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for…
This study establishes consistency conditions and a general solution for a coupled system that consists of five two-sided Sylvester-like tensor equations in ten quaternion variables throughout the Einstein tensor product. Certain specific…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
In this paper, we consider the mixed and componentwise condition numbers for a linear function of the solution to the linear least squares problem with equality constrains (LSE). We derive the explicit expressions of the mixed and…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
Information-theoretic generalization bounds analyze stochastic optimization by relating expected generalization error to the mutual information between learned parameters and training data. Virtual perturbation analyses of SGD add auxiliary…
We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
In this paper, we present a methodology for stability analysis of a general class of systems defined by coupled Partial Differential Equations (PDEs) with spatially dependent coefficients and a general class of boundary conditions. This…
The Generalized Chiral Perturbation Theory enlarges the framework of the standard $\chi$PT, relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low…
We analyze existence, uniqueness and regularity of solutions for perturbations of the Spence-Abel equation for the Rogers' dilogarithm. As an application we deduce a version of Hyers-Ulam stability for the Spence-Abel equation. Our analysis…
For a family of stabilized mixed finite element methods for the Stokes equations a complete a priori and a posteriori error analysis is given.
Perturbation expansions up to third order for the generalized spiked harmonic oscillator Hamiltonians H = -d^2/dx^2+ x^2 + A/x^2 + lambda/x^alpha, A >= 0, 2gamma > alpha, gamma=1+(1/2)sqrt(1+4A), and small values of the coupling lambda > 0,…
This review article discusses the experimental and theoretical status of various Parton Model sum rules. The basis of the sum rules in perturbative QCD is discussed. Their use in extracting the value of the strong coupling constant is…
Analytical perturbations of a family of finite-dimensional Poisson systems are considered. It is shown that the family is analytically orbitally conjugate in $U \subset \mathbb{R}^n$ to a planar harmonic oscillator defined on the symplectic…
The consideration of quantum fields defined on a spacetime lattice provides computational techniques which are invaluable for studying gauge theories nonperturbatively from first principles. Perturbation theory is an essential aspect of…
The problem of improving the reliability of perturbative QCD predictions at moderate energies is considered. These predictions suffer from substantial renormalization scheme dependence, which is illustrated using as an example the QCD…