2006/06/01 by Albrecht Boettcher, Jani A. Virtanen, Boettcher, Albrecht +1
Computer Science · Mathematics · Physics and Astronomy · #15A60 #47B35 #62M10 #65F35 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.math/0606016
openalex publication_date 2006/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.