相关论文: Correction of Errors in the First-Order Perturbati…
This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…
Embedded point spectra of rank one singular perturbations of an arbitrary self-adjoint operator A on a Hilbert space H is studied. It is shown that these perturbations can be regarded as self-adjoint extensions of a densely defined closed…
We provide first order perturbation formulas for the matrix square root (in the positive semi-definite case) and the matrix modulus (in the general case). The results are new for singular matrices, and extend previously known Fr\'{e}chet…
Estimating eigenvectors and low-dimensional subspaces is of central importance for numerous problems in statistics, computer science, and applied mathematics. This paper characterizes the behavior of perturbed eigenvectors for a range of…
A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank $1$ perturbation. Considered in this review are the additive rank $1$ perturbation of the…
We tabulate angularly reduced fourth-order many-body corrections to matrix elements for univalent atoms, derived in [A. Derevianko and E.D. Emmons, Phys. Rev. A 65, 052115 (2002)]. In particular we focused on practically important diagrams…
An upper bound for the number of distinct eigenvalues of a perturbed matrix has been recently established by P. E. Farrell [1, Theorem 1.3]. The estimate is the central result in Farrell's work and can be applied to estimate the number of…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
In two and three dimensions, we design and analyze a posteriori error estimators for the mixed Stokes eigenvalue problem. The unknowns on this mixed formulation are the pseudotress, velocity and pressure. With a lowest order mixed finite…
We perturb a real matrix $A$ of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our bounds, which extend existing lower-order expressions,…
Understanding the distributions of spectral estimators in low-rank random matrix models, also known as signal-plus-noise matrix models, is fundamentally important in various statistical learning problems, including network analysis, matrix…
Consider the multiple linear regression model $y_{i} = \boldsymbol{x}'_{i} \boldsymbol{\beta} + \epsilon_{i}$, where $\epsilon_i$'s are independent and identically distributed random variables, $\mathbf{x}_i$'s are known design vectors and…
We explicitly fix a mistake in a preliminary statement of our previous paper on the conductor at a multiplanar singularity. The correction is not immediate and, though the mistake does not affect correctness of the subsequent results, the…
The purpose of this note is to correct an inaccuracy in the paper: R.P. Agaev and P.Yu. Chebotarev, "On Determining the Eigenprojection and Components of a Matrix," Autom. Remote Control, 2002, vol. 63, pp. 1537-1545 [arXiv:math/0508197],…
Two typos in the published paper are pointed out. Both are just typos and the calculations in that paper are based on the correct formulism.
In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…
Recently, we discovered a mistake in our Letter on phase dynamics in granular d-wave superconductors, which we corrected in an Erratum published last week. This is an expanded version of the Erratum, containing details and supporting…
The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in…
The singular subspaces perturbation theory is of fundamental importance in probability and statistics. It has various applications across different fields. We consider two arbitrary matrices where one is a leave-one-column-out submatrix of…