{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T20:48:55Z","timestamp":1694119735609},"reference-count":30,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2020,9,15]],"date-time":"2020-09-15T00:00:00Z","timestamp":1600128000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,1]]},"abstract":"Abstract<\/jats:title>The singular value distribution of the matrix\u2010sequence {Y<\/jats:italic>n<\/jats:italic><\/jats:sub>T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>]}n<\/jats:italic><\/jats:sub><\/jats:styled-content>, with T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>]<\/jats:styled-content> generated by , was shown in [J. Pestana and A.J. Wathen, SIAM J Matrix Anal Appl. 2015;36(1):273\u2010288]. The results on the spectral distribution of {Y<\/jats:italic>n<\/jats:italic><\/jats:sub>T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>]}n<\/jats:italic><\/jats:sub><\/jats:styled-content> were obtained independently in [M. Mazza and J. Pestana, BIT, 59(2):463\u2010482, 2019] and [P. Ferrari, I. Furci, S. Hon, M.A. Mursaleen, and S. Serra\u2010Capizzano, SIAM J. Matrix Anal. Appl., 40(3):1066\u20101086, 2019]. In the latter reference, the authors prove that {Y<\/jats:italic>n<\/jats:italic><\/jats:sub>T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>]}n<\/jats:italic><\/jats:sub><\/jats:styled-content> is distributed in the eigenvalue sense as\nunder the assumptions that f<\/jats:italic> belongs to and has real Fourier coefficients. The purpose of this paper is to extend the latter result to matrix\u2010sequences of the form {h<\/jats:italic>(T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>])}n<\/jats:italic><\/jats:sub><\/jats:styled-content>, where h<\/jats:italic> is an analytic function. In particular, we provide the singular value distribution of the sequence {h<\/jats:italic>(T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>])}n<\/jats:italic><\/jats:sub><\/jats:styled-content>, the eigenvalue distribution of the sequence {Y<\/jats:italic>n<\/jats:italic><\/jats:sub>h<\/jats:italic>(T<\/jats:italic>n<\/jats:italic><\/jats:sub>[f<\/jats:italic>])}n<\/jats:italic><\/jats:sub><\/jats:styled-content>, and the conditions on f<\/jats:italic> and h<\/jats:italic> for these distributions to hold. Finally, the implications of our findings are discussed, in terms of preconditioning and of fast solution methods for the related linear systems.<\/jats:p>","DOI":"10.1002\/nla.2332","type":"journal-article","created":{"date-parts":[[2020,12,2]],"date-time":"2020-12-02T04:10:45Z","timestamp":1606882245000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic spectra of large matrices coming from the symmetrization of Toeplitz structure functions and applications to preconditioning"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-6615-7404","authenticated-orcid":false,"given":"Paola","family":"Ferrari","sequence":"first","affiliation":[{"name":"Dipartimento di Scienza ed Alta Tecnologia Universit\u00e0 dell'Insubria Como Italy"}]},{"given":"Nikos","family":"Barakitis","sequence":"additional","affiliation":[{"name":"Department of Informatics Athens University of Economics 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