{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:51:50Z","timestamp":1776721910910,"version":"3.51.2"},"reference-count":25,"publisher":"American Mathematical Society (AMS)","issue":"215","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The Arnoldi method computes eigenvalues of large nonsymmetric matrices. Restarting is generally needed to reduce storage requirements and orthogonalization costs. However, restarting slows down the convergence and makes the choice of the new starting vector difficult if several eigenvalues are desired. We analyze several approaches to restarting and show why Sorensen\u2019s implicit QR approach is generally far superior to the others. Ritz vectors are combined in precisely the right way for an effective new starting vector. Also, a new method for restarting Arnoldi is presented. It is mathematically equivalent to the Sorensen approach but has additional uses.<\/p>","DOI":"10.1090\/s0025-5718-96-00745-4","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1213-1230","source":"Crossref","is-referenced-by-count":132,"title":["On restarting the Arnoldi method for large nonsymmetric eigenvalue problems"],"prefix":"10.1090","volume":"65","author":[{"given":"Ronald","family":"Morgan","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","first-page":"623","article-title":"Annihilator ideals and representation iteration for abstract rings","volume":"5","author":"Everett, C. J., Jr.","year":"1939","journal-title":"Duke Math. 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