Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric

2010/08/06 by Yuji Nakatsukasa, Nakatsukasa, Yuji
Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Robotic Mechanisms and Dynamics #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.1008.1202

openalex publication_date 2010/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation
• Inclusion regions and bounds for the eigenvalues of matrices with a known eigenpair
• Generalized Eigenvalue Problems with Specified Eigenvalues
• Gershgorin disks for multiple eigenvalues of non-negative matrices
• Exclusion sets in eigenvalue inclusion sets for tensors