We consider the eigenvalues of a fixed, non-normal matrix subject to small additive perturbation. In particular, we case when fixed is banded Toeplitz matrix, where bandwidth allowed grow slowly with dimension, and perturbation drawn from one several different random ensembles. establish number non-asymptotic results for this model, including local law rate convergence in Wasserstein distance e...

The generalized Cholesky factorization and the Cholesky-like factorization are two generalizations of the classic Cholesky factorization. In this paper, the rigorous multiplicative perturbation bounds for the two factorizations are derived using the matrix equation and the refined matrix equation approaches. The corresponding first-order multiplicative perturbation bounds, as special cases, are...

Recent perturbation results for exponentially dichotomous operators are generalized, in part by replacing compactness conditions on the perturbation by resolvent compactness. Both additive and multiplicative perturbations are considered. Mathematics Subject Classification (2000). Primary 47D06; Secondary 47A55.

This paper contrastively researches the structural characteristic and the fission-evolution law of four different kinds of generalized Julia set generalized J set in short with different parameter c, which includes the generalized J set without any perturbation, the generalized J set perturbed by additive noises, the generalized J set perturbed by multiplicative noise, and the generalized J set...

The double angle theorems of Davis and Kahan bound the change in an invariant subspace when a Hermitian matrix A is subject to an additive perturbation A → Ã = A+1A. This paper supplies analogous results when A is subject to a congruential, or multiplicative, perturbation A → Ã = D∗AD. The relative gaps that appear in the bounds involve the spectrum of only one matrix, either A or Ã, in contras...