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Schiavoni-Piazza, Alec Jacopo Almo; Serra-Capizzano, Stefano

Distribution results for a special class of matrix sequences: joining approximation theory and asymptotic linear algebra. (English) Zbl 1521.15025

ETNA, Electron. Trans. Numer. Anal. 59, 1-8 (2023).
Summary: In a recent paper, D. S. Lubinsky [Linear Algebra Appl. 633, 332–365 (2022; Zbl 1478.15043)] proved eigenvalue distribution results for a class of Hankel matrix sequences arising in several applications, ranging from Padé approximation to orthogonal polynomials and complex analysis. The results appeared in Linear Algebra and its Applications, and indeed many of the statements, whose origin belongs to the field of approximation theory and complex analysis, contain deep results in (asymptotic) linear algebra. Here we make an analysis of a part of these findings by combining his derivation with previous results in asymptotic linear algebra, showing that the use of an already available machinery shortens considerably the considered part of the derivations. Remarks and few additional results are also provided, in the spirit of bridging (numerical and asymptotic) linear algebra results and those coming from analysis and pure approximation theory.

Cited in 1 Document

MSC:

15B05 Toeplitz, Cauchy, and related matrices
15A18 Eigenvalues, singular values, and eigenvectors
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
41A21 Padé approximation
41A10 Approximation by polynomials

Keywords:

Hankel matrix; Toeplitz matrix; matrix sequence; eigenvalue and singular value distribution; singular value clustering

Citations:

Zbl 1478.15043
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Full Text: DOI Link

References:

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