A useful variant of the Davis–Kahan theorem for statisticians

Studies in Borreliae Part 1. A variant of Borreliae parkeri Davis 1942 isolated in California and its tick vector

The Tan 2θ Theorem for Indefinite Quadratic Forms

A version of the Davis-Kahan Tan 2Θ theorem [SIAM J. Numer. Anal. 7 (1970), 1 – 46] for not necessarily semibounded linear operators defined by quadratic forms is proven. This theorem generalizes a recent result by Motovilov and Selin [Integr. Equat. Oper. Theory 56 (2006), 511 – 542].

Some Sharp Norm Estimates in the Subspace Perturbation Problem

We discuss the spectral subspace perturbation problem for a selfadjoint operator. Assuming that the convex hull of a part of its spectrum does not intersect the remainder of the spectrum, we establish an a priori sharp bound on variation of the corresponding spectral subspace under off-diagonal perturbations. This bound represents a new, a priori, tanΘ Theorem. We also extend the Davis–Kahan ta...

Large-scale Inversion of Magnetic Data Using Golub-Kahan Bidiagonalization with Truncated Generalized Cross Validation for Regularization Parameter Estimation

In this paper a fast method for large-scale sparse inversion of magnetic data is considered. The L1-norm stabilizer is used to generate models with sharp and distinct interfaces. To deal with the non-linearity introduced by the L1-norm, a model-space iteratively reweighted least squares algorithm is used. The original model matrix is factorized using the Golub-Kahan bidiagonalization that proje...

Unperturbed: spectral analysis beyond Davis-Kahan

Classical matrix perturbation results, such as Weyl’s theorem for eigenvalues andthe Davis-Kahan theorem for eigenvectors, are general purpose. These classicalbounds are tight in the worst case, but in many settings sub-optimal in the typicalcase. In this paper, we present perturbation bounds which consider the nature ofthe perturbation and its interaction with the unperturbed s...