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Comput."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>In this work, the infinite GMRES algorithm, recently proposed by [Jarlebring and Correnty, SIAM J. Matrix Anal. Appl., 43 (2022), pp. 1382\u20131405] is employed in contour integral-based nonlinear eigensolvers, avoiding the computation of costly factorizations at each quadrature node to solve the linear systems efficiently. Several techniques are applied to make the infinite GMRES memory-friendly, computationally efficient, and numerically stable in practice. More specifically, we analyze the relationship between polynomial eigenvalue problems and their scaled linearizations, and provide a novel weighting strategy which can significantly accelerate the convergence of infinite GMRES in this particular context. We also adopt the technique of TOAR to infinite GMRES to reduce the memory footprint. Theoretical analysis and numerical experiments are provided to illustrate the efficiency of the proposed algorithm.<\/jats:p>","DOI":"10.1137\/24m1650375","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T03:03:50Z","timestamp":1746414230000},"page":"B595-B617","source":"Crossref","is-referenced-by-count":1,"title":["Improving Performance of Contour Integral-Based Nonlinear Eigensolvers with Infinite GMRES"],"prefix":"10.1137","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9794-0973","authenticated-orcid":true,"given":"Yuqi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai, 200433 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1144-6772","authenticated-orcid":true,"given":"Jose E.","family":"Roman","sequence":"additional","affiliation":[{"name":"D. Sistemes Inform\u00e0tics i Computaci\u00f3, Universitat Polit\u00e8cnica de Val\u00e8ncia, Cam\u00ed de Vera s\/n, 46022 Val\u00e8ncia, Spain."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4914-7666","authenticated-orcid":true,"given":"Meiyue","family":"Shao","sequence":"additional","affiliation":[{"name":"School of Data Science and Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, 200433 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,5,5]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s13160-010-0005-x"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.14495\/jsiaml.1.52"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/140979927"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/070704769"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1145\/2427023.2427024"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.03.030"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.109.045414"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1145\/3447544"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00014-8"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/22M1502380"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2020.107509"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-012-0381-5"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019177600806"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596304563"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1364\/OL.42.001145"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2018.05.006"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/BF02510248"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492917000034"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/130935045"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1002\/nme.2076"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2023.128249"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/21M1410324"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/15M1044667"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-012-0453-0"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1913"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.36.000686"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/151005142"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1002\/gamm.201490007"},{"key":"ref29","unstructured":"X. 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