{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T09:01:02Z","timestamp":1784624462796,"version":"3.55.0"},"reference-count":36,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2026,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper considers the problem of computing the operator norm of a linear map between finite-dimensional Hilbert spaces when only evaluations of the linear map are available and under restrictive storage assumptions.\u00a0We propose a stochastic method of random search type to maximize the Rayleigh quotient and employ an exact line search in the random search directions. Moreover, we show that the proposed algorithm converges to the global maximum (the operator norm) almost surely and a sublinear convergence behavior for the corresponding eigenvector and eigenvalue equation. Finally, we illustrate the performance of the method with numerical experiments.<\/jats:p>","DOI":"10.1137\/25m1772277","type":"journal-article","created":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T08:01:12Z","timestamp":1784620872000},"page":"1349-1374","source":"Crossref","is-referenced-by-count":0,"title":["Matrix-Free Stochastic Calculation of Operator Norms Without Using Adjoints"],"prefix":"10.1137","volume":"47","author":[{"given":"Jonas","family":"Bresch","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Technical University Berlin, 10623 Berlin, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7419-769X","authenticated-orcid":true,"given":"Dirk A.","family":"Lorenz","sequence":"additional","affiliation":[{"name":"Center for Industrial Mathematics, Fachbereich 3, University of Bremen, 28334 Bremen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felix","family":"Schneppe","sequence":"additional","affiliation":[{"name":"Center for Industrial Mathematics, Fachbereich 3, University of Bremen, 28334 Bremen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8501-5556","authenticated-orcid":true,"given":"Maximilian","family":"Winkler","sequence":"additional","affiliation":[{"name":"Center for Industrial Mathematics, Fachbereich 3, University of Bremen, 28334 Bremen, Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,7,21]]},"reference":[{"key":"ref1","volume":"25","author":"Boull\u00e9 N.","year":"2024","journal-title":"J. Mach. Learn. Res."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/21M1448112"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/20M1326635"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2026.117853"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012085428800"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-010-0251-1"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011637511962"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/22M1490223"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/abd85c"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol55s213"},{"key":"ref11","first-page":"239","volume":"3","author":"Elezovi\u0107 N.","year":"2000","journal-title":"Math. Inequal. Appl."},{"key":"ref12","volume-title":"Proceedings of the International Fluid Dynamics Conference (AIAA)","author":"Fikl A.","year":"2016"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF00049302"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/0914029"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718720"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114352"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611976670"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.3934\/ipi.2026007"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595282519"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1525"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/0613066"},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"Y. Li, H. L. Nguyen, and D. P. Woodruff, On sketching matrix norms and the top singular vector, in Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), SIAM, Philadelphia, 2014, pp. 1562\u20131581, https:\/\/doi.org\/10.1137\/1.9781611973402.114.","DOI":"10.1137\/1.9781611973402.114"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-018-0717-x"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-022-09933-5"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6420\/ad08ed"},{"key":"ref27","unstructured":"M. Magdon-Ismail, A Note on Estimating the Spectral Norm of a Matrix Efficiently, https:\/\/doi.org\/10.48550\/arXiv.1104.2076, 2011."},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492920000021"},{"key":"ref29","doi-asserted-by":"crossref","unstructured":"E. Naldi and F. Schneppe, The Influence of an Adjoint Mismatch on the Primal-Dual Douglas\u2013Rachford Method, https:\/\/doi.org\/10.48550\/arXiv.2503.24141, 2025.","DOI":"10.1080\/02331934.2026.2692689"},{"key":"ref30","volume-title":"Wahrscheinlichkeitsrechnung, Hochschulb\u00fccher f\u00fcr Mathematik","author":"R\u00e9nyi A.","year":"1966","edition":"2"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1017\/9781009160865"},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"M. Savanier, \u00c9. Chouzenoux, J.C. Pesquet, C. Riddell, and Y. Trousset, Proximal gradient algorithm in the presence of adjoint mismatch, in Proceedings of the 28th European Signal Processing Conference (EUSIPCO), 2021, pp. 2140\u20132144, https:\/\/doi.org\/10.23919\/Eusipco47968.2020.9287430.","DOI":"10.23919\/Eusipco47968.2020.9287430"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/0910004"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1364\/OE.24.025129"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.7717\/peerj.453"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1109\/42.870265"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T08:01:19Z","timestamp":1784620879000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1772277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,21]]},"references-count":36,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2026,9,30]]}},"alternative-id":["10.1137\/25M1772277"],"URL":"https:\/\/doi.org\/10.1137\/25m1772277","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,21]]}}}