{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T23:38:02Z","timestamp":1776728282502,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,5,14]],"date-time":"2002-05-14T00:00:00Z","timestamp":1021334400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates.<\/p>","DOI":"10.1090\/s0025-5718-01-01324-2","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"479-505","source":"Crossref","is-referenced-by-count":142,"title":["Analysis of iterative methods for saddle point problems: a unified approach"],"prefix":"10.1090","volume":"71","author":[{"given":"Walter","family":"Zulehner","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,5,14]]},"reference":[{"key":"1","series-title":"Stanford Mathematical Studies in the Social Sciences, II","volume-title":"Studies in linear and non-linear programming","author":"Arrow, Kenneth J.","year":"1958"},{"issue":"7","key":"2","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1007\/BF01405194","article-title":"A class of iterative methods for solving saddle point problems","volume":"56","author":"Bank, Randolph E.","year":"1990","journal-title":"Numer. 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