How well-conditioned can the eigenvalue problem be?

2021/05/17 by Carlos Beltrán, Laurent Bétermin, Beltrán, Carlos +5
Computer Science · Mathematics · #31C20 (Secondary) #65F15 (Primary) #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2105.07922

openalex publication_date 2021/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalue computations? In this note we answer this question with exact first order asymptotic.

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