This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

This work is concerned with numerical methods for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In particular, we focus on eigenvalue problems for which the evaluation of the matrix valued function is computationally expensive. Such problems arise, e.g., from boundary integral formulations of elliptic PDE-eigenvalue problems and typically exclude the use of establis...

Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve eigenproblems. rIGA discretization, while conserving desirable properties maximum-continuity (IGA), reduces interconnection between degrees freedom by adding low-continuity basis functions. This connectivity reduction in rIGA’s alge...

We present Gerschgorin-type eigenvalue inclusion sets applicable to generalized eigenvalue problems. Our sets are defined by circles in the complex plane in the standard Euclidean metric, and are easier to compute than known similar results. As one application we use our results to provide a forward error analysis for a computed eigenvalue of a diagonalizable pencil.

This paper concerns with the sensitivity analysis for the multivariate eigenvalue problem (MEP). The concept of a simple multivariate eigenvalue of a matrix is generalized to the MEP and the first-order perturbation expansions of a simple multivariate eigenvalue and the corresponding multivariate eigenvector are presented. The explicit expressions of condition numbers, perturbation upper bounds...

There are two cases where it is well known that Schriidinger operators have non-degenerate eigenvalues: The lowest eigenvalue in general dimension and all one-dimensional eigenvalues. One can ask about making this quantitative, i.e., obtain explicit lower bounds on the distance to the nearest eigenvalues. Obviously, one cannot hope to do this without any restrictions on V since, for example, if...