{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:37Z","timestamp":1787337217034,"version":"3.56.0"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>Large 2-level Toeplitz systems arise in a variety of applications (see, e.g., [R. H. Chan and M. Ng, SIAM Rev., 38 (1996), pp. 427-482]) for which efficient numerical methods for their solution are required. Some successful numerical techniques need the explicit knowledge of the generating function f of the considered system $T_{n}(f){\\rm x}=b$, an assumption that usually is not fulfilled in real applications. In this paper we analyze and complete the procedure proposed in [D. Noutsas, S. Serra Capizzano, and P. Vassalos, Numer. Linear Algebra Appl., 12 (2005), pp. 231-239] for the 2-level case. In such a way, from the knowledge of the coefficients of $T_{n}(f)$, we determine optimal preconditioning strategies for the solution of our systems. Finally, some numerical experiments are performed and discussed in connection with our theoretical analysis.<\/jats:p>","DOI":"10.1137\/050627046","type":"journal-article","created":{"date-parts":[[2006,4,3]],"date-time":"2006-04-03T21:00:16Z","timestamp":1144098016000},"page":"439-458","source":"Crossref","is-referenced-by-count":7,"title":["Two-level Toeplitz preconditioning: approximation results for matrices and functions"],"prefix":"10.1137","volume":"28","author":[{"given":"D.","family":"Noutsos","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S. 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