相关论文: Correction of Errors in the First-Order Perturbati…

This work analyzes singular-value spectra of weight matrices in pretrained transformer models to understand how information is stored at both ends of the spectrum. Using Random Matrix Theory (RMT) as a zero information hypothesis, we…

We prove a comprehensive solution theory using tools from functional analysis, show corresponding variational formulations, and present functional a posteriori error estimates for general linear first order systems. As a prototypical…

A conjecture from a paper by J. Bierkens and A.C.M. Ran concerning the location of eigenvalues of rank one perturbations of singular M-matrices is shown to be false in dimension four and higher, but true for dimension two, as well as for…

We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of…

Eigenvalue and eigenvector perturbation theory is a fundamental topic in several disciplines, including numerical linear algebra, quantum physics, and related fields. The central problem is to understand how the eigenvalues and eigenvectors…

Perturbation analysis has emerged as a significant concern across multiple disciplines, with notable advancements being achieved, particularly in the realm of matrices. This study centers on specific aspects pertaining to tensor…

We develop new perturbation techniques for conducting convergence analysis of various first-order algorithms for a class of nonsmooth optimization problems. We consider the iteration scheme of an algorithm to construct a perturbed…

This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed…

In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation…

The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by…

The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…

In this paper, we present a posteriori error estimation for weak Galerkin method applied to fourth order singularly perturbed problem. The weak Galerkin discretization space and numerical scheme are first described. A fully computable…

Recently, Stewart gave an algorithm for computing a rank revealing URV decomposition of a rectangular matrix. His method makes use of a refinement iteration to achieve an improved estimate of the smallest singular value and its…

The second edition of the book "Roos, Stynes, Tobiska -- Robust Numerical Methods for Singularly Perturbed Differential Equations" appeared many years ago and was for many years a reliable guide into the world of numerical methods for…

The work is devoted to the study of Laplace operator when the potential is a singular generalized function and plays the role of a singular perturbation of a Laplace operator. Abstract theorem obtained earlier by the authors B.N. Biyarov…

We study an ensemble of random matrices (the Rosenzweig-Porter model) which, in contrast to the standard Gaussian ensemble, is not invariant under changes of basis. We show that a rather complete understanding of its level correlations can…

Correction to The Annals of Statistics (2006) 34, 1013--1044 [URL: http://projecteuclid.org/euclid.aos/1151418250]

In this article I study different possibilities of analytically solving the Sturm-Liouville problem with variable coefficients of sufficiently arbitrary behavior with help of perturbation theory. I show how the problem can be reformulated…

Correction on Moments of minors of Wishart matrices by M. Drton and A. Goia (Ann. Statist. 36 (2008) 2261-2283), arXiv:math/0604488

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…