{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T11:27:14Z","timestamp":1776079634674,"version":"3.50.1"},"reference-count":40,"publisher":"American Mathematical Society (AMS)","issue":"351","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2306438"],"award-info":[{"award-number":["DMS-2306438"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We study the GMRES algorithm applied to linear systems of equations involving a scaled and shifted <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N times upper N\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>N<\/mml:mi>\n      <mml:mo>\u00d7<\/mml:mo>\n      <mml:mi>N<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">N\\times N<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> matrix whose entries are independent complex Gaussians. When the right-hand side of this linear system is independent of this random matrix, the <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N right-arrow normal infinity\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>N<\/mml:mi>\n      <mml:mo stretchy=\"false\">\u2192<\/mml:mo>\n      <mml:mi mathvariant=\"normal\">\u221e<\/mml:mi>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">N\\to \\infty<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> behavior of the GMRES residual error can be determined exactly. To handle cases where the right hand side depends on the random matrix, we study the pseudospectra and numerical range of Ginibre matrices and prove a restricted version of Crouzeix\u2019s conjecture.<\/p>","DOI":"10.1090\/mcom\/3963","type":"journal-article","created":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T00:18:25Z","timestamp":1709943505000},"page":"241-261","source":"Crossref","is-referenced-by-count":3,"title":["GMRES, pseudospectra, and Crouzeix\u2019s conjecture for shifted and scaled Ginibre matrices"],"prefix":"10.1090","volume":"94","author":[{"given":"Tyler","family":"Chen","sequence":"first","affiliation":[]},{"given":"Anne","family":"Greenbaum","sequence":"additional","affiliation":[]},{"given":"Thomas","family":"Trogdon","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,3,25]]},"reference":[{"issue":"2","key":"1","first-page":"863","article-title":"Convergence to the semicircle law","volume":"16","author":"Bai, Z. 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