We consider elliptic PDE eigenvalue problems on a tensorized domain, discretized such that
the resulting matrix eigenvalue problem Ax= λx exhibits Kronecker product structure. In …

We present two theoretical results for the linear response eigenvalue problem. The first
result is a minimization principle for the sum of the smallest eigenvalues with the positive …

In this paper, strong relative perturbation bounds are developed for a number of linear
algebra problems involving diagonally dominant matrices. The key point is to parameterize …

This work introduces a new perturbation bound for the L factor of the LDU factorization of
(row) diagonally dominant matrices computed via the column diagonal dominance pivoting …

Generalized eigendecomposition, which extracts the generalized eigenvector from a matrix
pencil, is a powerful tool and has been widely used in many fields, such as data …

This paper contributes to the perturbation theory for parameter dependent quadratic
eigenvalue problems (PQEP). Specifically, we derive an approximate perturbation bound …

This paper presents an approach to the efficient calculation of all or just one important part of
the eigenvalues of the parameter dependent quadratic eigenvalue problem (λ 2 (v) M+ λ (v) …

In this paper, we consider the generalized eigenvalue problem (GEP) for bidiagonal-product
(BP) pairs with sign regularity (SR), which include structured pairs associated with ill …

Heavily damped quadratic eigenvalue problem (QEP) is a special type of QEPs. It has a
large gap between small and large eigenvalues in absolute value. One common way for …

When a symmetric block diagonal matrix A 1 A 2\big undergoes an off-diagonal perturbation
A 1 E 12 E 12 TA 2,\big, the eigenvalues of these matrices are known to differ only by O (∥ E …