Alec Jacopo Almo Schiavoni-Piazza,
Stefano Serra-Capizzano
S. 1 - 8
doi:
10.1553/etna_vol59s1
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol59s1
Abstract:
In a recent paper, Lubinsky 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.
Hankel and Toeplitz matrix, matrix sequence, eigenvalue and singular value distribution, eigenvalue and singular value clustering
Published Online:
2022/11/15 09:10:40
Object Identifier:
0xc1aa5572 0x003dd153
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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