{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:24:22Z","timestamp":1740108262179,"version":"3.37.3"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,10,1]],"date-time":"2024-10-01T00:00:00Z","timestamp":1727740800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math Meth Oper Res"],"published-print":{"date-parts":[[2024,10]]},"DOI":"10.1007\/s00186-024-00866-z","type":"journal-article","created":{"date-parts":[[2024,10,7]],"date-time":"2024-10-07T12:07:29Z","timestamp":1728302849000},"page":"411-435","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["How to project onto the intersection of a closed affine subspace and a hyperplane"],"prefix":"10.1007","volume":"100","author":[{"given":"Heinz H.","family":"Bauschke","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dayou","family":"Mao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0113-9309","authenticated-orcid":false,"given":"Walaa M.","family":"Moursi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,7]]},"reference":[{"key":"866_CR1","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s00186-019-00691-9","volume":"91","author":"FJ Arag\u00f3n Artacho","year":"2020","unstructured":"Arag\u00f3n Artacho FJ, Campoy R, Tam MK (2020) The Douglas-Rachford algorithm for convex and nonconvex feasibility problems. Math Methods Opera Res 91:201\u2013240","journal-title":"Math Methods Opera Res"},{"key":"866_CR2","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1006\/jath.1994.1136","volume":"79","author":"HH Bauschke","year":"1994","unstructured":"Bauschke HH, Borwein JM (1994) Dykstra\u2019s alternating projection algorithm for two sets. J Approx Theory 79:418\u2013443","journal-title":"J Approx Theory"},{"key":"866_CR3","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BF01027691","volume":"1","author":"HH Bauschke","year":"1993","unstructured":"Bauschke HH, Borwein JM (1993) On the convergence of von Neumann\u2019s alternating projection algorithm for two sets. Set-Valued Anal 1:185\u2013212","journal-title":"Set-Valued Anal"},{"key":"866_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-48311-5","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2017","unstructured":"Bauschke HH, Combettes PL (2017) Convex Analysis and Monotone Operator Theory in Hilbert Spaces, 2nd edn. Springer","edition":"2"},{"key":"866_CR5","doi-asserted-by":"publisher","DOI":"10.1186\/s13663-021-00708-1","author":"HH Bauschke","year":"2021","unstructured":"Bauschke HH, Singh S, Wang X (2021) Projecting onto rectangular matrices with prescribed row and column sums. Fixed Point Theory Algorithms Sci Eng. https:\/\/doi.org\/10.1186\/s13663-021-00708-1","journal-title":"Fixed Point Theory Algorithms Sci Eng"},{"key":"866_CR6","doi-asserted-by":"publisher","first-page":"1475","DOI":"10.1007\/s11075-020-00941-6","volume":"86","author":"R Behling","year":"2021","unstructured":"Behling R, Bello-Cruz J-Y, Santos L-R (2021) On the circumcentered-reflection method for the convex feasibility problem. Numer Algorithms 86:1475\u20131494","journal-title":"Numer Algorithms"},{"issue":"1","key":"866_CR7","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1137\/141000671","volume":"59","author":"J Bezanson","year":"2017","unstructured":"Bezanson J, Edelman A, Karpinski S, Shah VB (2017) Julia: a fresh approach to numerical computing. SIAM Rev 59(1):65\u201398. https:\/\/doi.org\/10.1137\/141000671","journal-title":"SIAM Rev"},{"key":"866_CR8","volume-title":"Parallel Optimization","author":"Y Censor","year":"1997","unstructured":"Censor Y, Zenios SA (1997) Parallel Optimization. Oxford University Press, Oxford"},{"key":"866_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9298-9","volume-title":"Best Approximation in Inner Product Spaces","author":"F Deutsch","year":"2001","unstructured":"Deutsch F (2001) Best Approximation in Inner Product Spaces. Springer, Cham"},{"key":"866_CR10","doi-asserted-by":"crossref","unstructured":"Escalante R, Raydan M (2011) Alternating Projection Methods. SIAM","DOI":"10.1137\/1.9781611971941"},{"key":"866_CR11","unstructured":"Geogebra, http:\/\/www.geogebra.org"},{"key":"866_CR12","doi-asserted-by":"crossref","unstructured":"Glunt W, Hayden TL, Reams R (1998) The nearest doubly stochastic\u201d matrix to a real matrix with the same first moment. Numer Linear Algebra Appl 5:475\u2013482","DOI":"10.1002\/(SICI)1099-1506(199811\/12)5:6<475::AID-NLA155>3.0.CO;2-5"},{"key":"866_CR13","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1590\/S0101-82052008000200005","volume":"27","author":"W Glunt","year":"2008","unstructured":"Glunt W, Hayden TL, Reams R (2008) The nearest generalized doubly stochastic matrix to a real matrix with the same first and second moments. Comput Appl Math 27:201\u2013210","journal-title":"Comput Appl Math"},{"key":"866_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0041-5553(67)90113-9","volume":"7","author":"LG Gubin","year":"1967","unstructured":"Gubin LG, Polyak BT, Raik EV (1967) The method of projections for finding the common point of convex sets. USSR Comput Math Math Phys 7:1\u201314","journal-title":"USSR Comput Math Math Phys"},{"key":"866_CR15","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/s11075-017-0430-x","volume":"79","author":"PC Hansen","year":"2017","unstructured":"Hansen PC, J\u00f8rgensen JS, Tools AIR II (2017) algebraic iterative reconstruction methods, improved implementation. Numer Algorithms 79:107\u2013137","journal-title":"Numer Algorithms"},{"key":"866_CR16","volume-title":"Fundamentals of Computerized Tomography","author":"GT Herman","year":"2010","unstructured":"Herman GT (2010) Fundamentals of Computerized Tomography, 2nd edn. Springer, Cham","edition":"2"},{"key":"866_CR17","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1006\/jmaa.1998.5970","volume":"222","author":"RN Khoury","year":"1998","unstructured":"Khoury RN (1998) Closest matrices in the space of generalized doubly stochastic matrices. J Math Anal Appl 222:561\u2013568","journal-title":"J Math Anal Appl"},{"key":"866_CR18","volume-title":"Introductory Functional Analysis and Applications","author":"E Kreyszig","year":"1989","unstructured":"Kreyszig E (1989) Introductory Functional Analysis and Applications. Wiley, London"},{"key":"866_CR19","first-page":"116","volume":"18","author":"W L\u00f3pez","year":"2018","unstructured":"L\u00f3pez W (2018) A new way of computing the orthogonal projection onto the intersection of two hyperplanes in a finite-dimensional Hilbert space. Appl Math E-Notes 18:116\u2013123","journal-title":"Appl Math E-Notes"},{"key":"866_CR20","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/s00041-012-9248-z","volume":"19","author":"D Needell","year":"2013","unstructured":"Needell D, Ward R (2013) Two-subspace projection method for coherent overdetermined systems. J Fourier Anal Appl 19:256\u2013269","journal-title":"J Fourier Anal Appl"},{"key":"866_CR21","first-page":"857","volume":"29","author":"H Ouyang","year":"2022","unstructured":"Ouyang H (2022) Finite convergence of locally proper circumcentered methods. J Convex Anal 29:857\u2013892","journal-title":"J Convex Anal"},{"key":"866_CR22","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1109\/TNS.1974.6499235","volume":"21","author":"LA Shepp","year":"1974","unstructured":"Shepp LA, Logan BF (1974) The Fourier reconstruction of a head section. IEEE Trans Nuclear Sci 21:21\u201343","journal-title":"IEEE Trans Nuclear Sci"}],"container-title":["Mathematical Methods of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-024-00866-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00186-024-00866-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00186-024-00866-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T10:11:48Z","timestamp":1728987108000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00186-024-00866-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["866"],"URL":"https:\/\/doi.org\/10.1007\/s00186-024-00866-z","relation":{},"ISSN":["1432-2994","1432-5217"],"issn-type":[{"type":"print","value":"1432-2994"},{"type":"electronic","value":"1432-5217"}],"subject":[],"published":{"date-parts":[[2024,10]]},"assertion":[{"value":"25 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 October 2024","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest for this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}