{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:43:22Z","timestamp":1776840202072,"version":"3.51.2"},"reference-count":46,"publisher":"American Mathematical Society (AMS)","issue":"355","license":[{"start":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:00:00Z","timestamp":1760054400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004543","name":"China Scholarship Council","doi-asserted-by":"publisher","award":["202306920044"],"award-info":[{"award-number":["202306920044"]}],"id":[{"id":"10.13039\/501100004543","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan\u2019s sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational approximation algorithms, such as the adaptive Antoulas-Anderson (AAA), AAA-Lawson, and the rational Krylov fitting method, perform highly efficiently, but the computed rational approximations may not be minimax solutions. In this paper, we propose a convex programming approach, the solution of which is guaranteed to be the rational minimax approximation under Ruttan\u2019s sufficient condition. Furthermore, we present a new version of Lawson\u2019s iteration for solving this convex programming problem. The computed solution can be easily verified as the rational minimax approximation. Our numerical experiments demonstrate that this updated version of Lawson\u2019s iteration generally converges monotonically with respect to the objective function of the convex optimization. It is an effective competitive approach for computing the rational minimax approximation, compared to the highly efficient AAA, AAA-Lawson, and the stabilized Sanathanan-Koerner iteration.<\/p>","DOI":"10.1090\/mcom\/4021","type":"journal-article","created":{"date-parts":[[2024,10,4]],"date-time":"2024-10-04T12:55:49Z","timestamp":1728046549000},"page":"2457-2494","source":"Crossref","is-referenced-by-count":3,"title":["A convex dual problem for the rational minimax approximation and Lawson\u2019s iteration"],"prefix":"10.1090","volume":"94","author":[{"given":"Lei-Hong","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Linyi","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Wei Hong","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Ya-Nan","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,10,10]]},"reference":[{"key":"1","series-title":"Translations of Mathematical Monographs","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1090\/mmono\/079","volume-title":"Elements of the theory of elliptic functions","volume":"79","author":"Akhiezer, N. 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