{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T03:33:11Z","timestamp":1777865591809,"version":"3.51.4"},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12471377"],"award-info":[{"award-number":["12471377"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2022YFA1004403"],"award-info":[{"award-number":["2022YFA1004403"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["22DZ2229014"],"award-info":[{"award-number":["22DZ2229014"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.cam.2026.117602","type":"journal-article","created":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T16:09:36Z","timestamp":1773504576000},"page":"117602","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["On averaged block nonlinear Kaczmarz method with adaptive step size for solving systems of nonlinear equations"],"prefix":"10.1016","volume":"485","author":[{"given":"Shuni","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Longze","family":"Tan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8571-2271","authenticated-orcid":false,"given":"Xueping","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117602_bib0001","series-title":"Methods for solving systems of nonlinear equations","author":"Rheinboldt","year":"1998"},{"issue":"4","key":"10.1016\/j.cam.2026.117602_bib0002","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1137\/0715050","article-title":"On Newton-iterative methods for the solution of systems of nonlinear equations","volume":"15","author":"Sherman","year":"1978","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.cam.2026.117602_bib0003","first-page":"355","article-title":"Angenaherte auflosung von systemen linearer glei-chungen","author":"Karczmarz","year":"1937","journal-title":"Bull. Int. Acad. Pol. Sic. Let. Cl. Sci. Math. Nat."},{"issue":"2","key":"10.1016\/j.cam.2026.117602_bib0004","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/s00041-008-9030-4","article-title":"A randomized Kaczmarz algorithm with exponential convergence","volume":"15","author":"Strohmer","year":"2009","journal-title":"J. Fourier Anal. Appl."},{"key":"10.1016\/j.cam.2026.117602_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113720","article-title":"Nonlinear Kaczmarz algorithms and their convergence","volume":"399","author":"Wang","year":"2022","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0006","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2023.115065","article-title":"On maximum residual nonlinear Kaczmarz-type algorithms for large nonlinear systems of equations","volume":"425","author":"Zhang","year":"2023","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0007","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01396365","article-title":"Block-iterative methods for consistent and inconsistent linear equations","volume":"35","author":"Elfving","year":"1980","journal-title":"Numer. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0008","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1016\/j.laa.2015.06.027","article-title":"Randomized block Kaczmarz method with projection for solving least squares","volume":"484","author":"Needell","year":"2015","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.cam.2026.117602_bib0009","article-title":"On the error estimate of the randomized double block Kaczmarz method","volume":"370","author":"Chen","year":"2020","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"10.1016\/j.cam.2026.117602_bib0010","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/s13160-023-00620-8","article-title":"On pseudoinverse-free block maximum residual nonlinear Kaczmarz method for solving large-scale nonlinear system of equations","volume":"41","author":"Zhang","year":"2024","journal-title":"Jpn. J. Ind. Appl. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117602_bib0011","doi-asserted-by":"crossref","first-page":"954","DOI":"10.1007\/s42967-024-00427-5","article-title":"On a nonlinear fast deterministic block Kaczmarz method for solving nonlinear equations","volume":"7","author":"Tan","year":"2025","journal-title":"Commun. Appl. Math. Comput."},{"issue":"3","key":"10.1016\/j.cam.2026.117602_bib0012","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1007\/s11075-021-01143-4","article-title":"On a fast deterministic block Kaczmarz method for solving large-scale linear systems","volume":"89","author":"Chen","year":"2022","journal-title":"Numer. Algo."},{"issue":"1","key":"10.1016\/j.cam.2026.117602_bib0013","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1137\/21M1463306","article-title":"A deterministic Kaczmarz algorithm for solving linear systems","volume":"44","author":"Shao","year":"2023","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.cam.2026.117602_bib0014","article-title":"On convergence of greedy block nonlinear Kaczmarz methods with momentum","volume":"478","author":"Jiang","year":"2025","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0015","first-page":"1","article-title":"On stochastic block methods for solving nonlinear equations","author":"Bao","year":"2025","journal-title":"Numer. Algo."},{"key":"10.1016\/j.cam.2026.117602_bib0016","article-title":"A stochastic column-block gradient descent method for solving nonlinear systems of equations","author":"Jiang","year":"2025","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.cam.2026.117602_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2024.116328","article-title":"On the adaptive deterministic block Kaczmarz method with momentum for solving large-scale consistent linear systems","volume":"457","author":"Tan","year":"2025","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0018","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.laa.2012.12.022","article-title":"Paved with good intentions: analysis of a randomized block Kaczmarz method","volume":"441","author":"Needell","year":"2014","journal-title":"Linear Algebra Appl."},{"issue":"4","key":"10.1016\/j.cam.2026.117602_bib0019","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1137\/19M1251643","article-title":"Faster randomized block Kaczmarz algorithms","volume":"40","author":"Necoara","year":"2019","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.cam.2026.117602_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2020.106294","article-title":"A greedy block Kaczmarz algorithm for solving large-scale linear systems","volume":"104","author":"Niu","year":"2020","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"10.1016\/j.cam.2026.117602_bib0021","doi-asserted-by":"crossref","first-page":"6792","DOI":"10.3934\/math.2022378","article-title":"A greedy average block Kaczmarz method for the large scaled consistent system of linear equations","volume":"7","author":"Wen","year":"2022","journal-title":"AIMS Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117602_bib0022","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s40314-023-02232-x","article-title":"On fast greedy block Kaczmarz methods for solving large consistent linear systems","volume":"42","author":"Xiao","year":"2023","journal-title":"Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117602_bib0023","doi-asserted-by":"crossref","DOI":"10.1016\/j.aml.2023.108704","article-title":"A surrogate hyperplane Kaczmarz method for solving consistent linear equations","volume":"144","author":"Wang","year":"2023","journal-title":"Appl. Math. Lett."},{"issue":"6","key":"10.1016\/j.cam.2026.117602_bib0024","doi-asserted-by":"crossref","DOI":"10.1137\/20M1312629","article-title":"Randomized extended average block Kaczmarz for solving least squares","volume":"42","author":"Du","year":"2020","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.cam.2026.117602_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2022.114372","article-title":"On greedy randomized average block Kaczmarz method for solving large linear systems","volume":"413","author":"Miao","year":"2022","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117602_bib0026","doi-asserted-by":"crossref","first-page":"289","DOI":"10.3934\/ipi.2007.1.289","article-title":"Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis","volume":"1","author":"Haltmeier","year":"2007","journal-title":"Inverse Probl. Imaging"},{"issue":"5","key":"10.1016\/j.cam.2026.117602_bib0027","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1007\/s40314-024-02797-1","article-title":"A residual-based weighted nonlinear Kaczmarz method for solving nonlinear systems of equations","volume":"43","author":"Ye","year":"2024","journal-title":"Comput. Appl. Math."},{"issue":"2","key":"10.1016\/j.cam.2026.117602_bib0028","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10092-024-00577-1","article-title":"Greedy randomized sampling nonlinear Kaczmarz methods","volume":"61","author":"Zhang","year":"2024","journal-title":"Calcolo"},{"issue":"7","key":"10.1016\/j.cam.2026.117602_bib0029","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1063\/1.524647","article-title":"Solution of the Chandrasekhar H-equation by Newton\u2019s method","volume":"21","author":"Kelley","year":"1980","journal-title":"J. Math. Phys."},{"issue":"2","key":"10.1016\/j.cam.2026.117602_bib0030","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1137\/0913025","article-title":"Comparing algorithms for solving sparse nonlinear systems of equations","volume":"13","author":"Gomes-Ruggiero","year":"1992","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"4","key":"10.1016\/j.cam.2026.117602_bib0031","first-page":"305","article-title":"Inexact trust region method for large sparse nonlinear least squares","volume":"29","author":"Luk\u0161an","year":"1993","journal-title":"Kybernetika"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002451?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002451?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T06:57:04Z","timestamp":1777532224000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726002451"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":31,"alternative-id":["S0377042726002451"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117602","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On averaged block nonlinear Kaczmarz method with adaptive step size for solving systems of nonlinear equations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117602","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117602"}}