{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:46:43Z","timestamp":1759042003611},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,6,23]],"date-time":"2015-06-23T00:00:00Z","timestamp":1435017600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2016,1]]},"DOI":"10.1007\/s10589-015-9768-y","type":"journal-article","created":{"date-parts":[[2015,6,22]],"date-time":"2015-06-22T06:08:51Z","timestamp":1434953331000},"page":"29-44","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An acceleration scheme for Dykstra\u2019s algorithm"],"prefix":"10.1007","volume":"63","author":[{"given":"Williams","family":"L\u00f3pez","sequence":"first","affiliation":[]},{"given":"Marcos","family":"Raydan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,6,23]]},"reference":[{"key":"9768_CR1","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.2514\/2.515","volume":"36","author":"MO Abdalla","year":"1998","unstructured":"Abdalla, M.O., Grigoriadis, K.M., Zimmerman, D.C.: Enhanced structural damage detection using alternating projection methods. AIAA J. 36, 1305\u20131311 (1998)","journal-title":"AIAA J."},{"key":"9768_CR2","first-page":"253","volume":"20","author":"G Appleby","year":"2005","unstructured":"Appleby, G., Smolarski, D.: A linear acceleration row action method for projecting onto subspaces. Electron. Trans. Numer. Anal. 20, 253\u2013275 (2005)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"9768_CR3","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1006\/jath.1994.1136","volume":"79","author":"HH Bauschke","year":"1994","unstructured":"Bauschke, H.H., Borwein, J.M.: Dykstra\u2019s alternating projection algorithm for two sets. J. Approx. Theory 79, 418\u2013443 (1994)","journal-title":"J. Approx. Theory"},{"key":"9768_CR4","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1137\/S0036144593251710","volume":"38","author":"HH Bauschke","year":"1996","unstructured":"Bauschke, H.H., Borwein, J.M.: On projection algorithms for solving convex feasibility problems. SIAM Rev. 38, 367\u2013426 (1996)","journal-title":"SIAM Rev."},{"key":"9768_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex Analysis and Monotone Operator Theory in Hilbert Spaces","author":"HH Bauschke","year":"2011","unstructured":"Bauschke, H.H., Combettes, P.L.: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011)"},{"key":"9768_CR6","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s11075-005-9010-6","volume":"41","author":"HH Bauschke","year":"2006","unstructured":"Bauschke, H.H., Combettes, P.L., Kruk, S.G.: Extrapolation algorithm for affine-convex feasibility problems. Numer. Algorithms 41, 239\u2013274 (2006)","journal-title":"Numer. Algorithms"},{"key":"9768_CR7","doi-asserted-by":"crossref","first-page":"3433","DOI":"10.1090\/S0002-9947-03-03136-2","volume":"355","author":"HH Bauschke","year":"2003","unstructured":"Bauschke, H.H., Deutsch, F., Hundal, H., Park, S.H.: Accelerating the convergence of the method of alternating projections. Trans. Am. Math. Soc. 355, 3433\u20133461 (2003)","journal-title":"Trans. Am. Math. Soc."},{"key":"9768_CR8","first-page":"1405","volume":"26","author":"EG Birgin","year":"2005","unstructured":"Birgin, E.G., Raydan, M.: Robust stopping criteria for Dykstra\u2019s algorithm, SIAM. J. Sci. Comput. 26, 1405\u20131414 (2005)","journal-title":"J. Sci. Comput."},{"key":"9768_CR9","doi-asserted-by":"crossref","unstructured":"Boyle, J.P., Dykstra, L.: A method for finding projections onto the intersections of convex sets in Hilbert spaces. In: Advances in Order Restricted Statistical Inference. Lecture Notes in Statistics, vol. 37, pp. 28\u201347. Springer, Berlin (1985)","DOI":"10.1007\/978-1-4613-9940-7_3"},{"key":"9768_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10957-013-0381-x","volume":"160","author":"JM Borwein","year":"2014","unstructured":"Borwein, J.M., Tam, M.K.: A cyclic Douglas\u2013Rachford iteration scheme. J. Optim. Theory Appl. 160, 1\u201329 (2014)","journal-title":"J. Optim. Theory Appl."},{"key":"9768_CR11","first-page":"319","volume":"6","author":"LM Bregman","year":"1999","unstructured":"Bregman, L.M., Censor, Y., Reich, S.: Dykstra\u2019s algorithm as the nonlinear extension of Bregman\u2019s optimization method. J. Convex Anal. 6, 319\u2013333 (1999)","journal-title":"J. Convex Anal."},{"key":"9768_CR12","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.jat.2003.08.004","volume":"124","author":"LM Bregman","year":"2003","unstructured":"Bregman, L.M., Censor, Y., Reich, S., Zepkowitz-Malachi, Y.: Finding the projection of a point onto the intersection of convex sets via the projection onto halfspaces. J. Approx. Theory 124, 194\u2013218 (2003)","journal-title":"J. Approx. Theory"},{"key":"9768_CR13","doi-asserted-by":"crossref","unstructured":"Cegielski, A.: Iterative Methods for Fixed Point Problems in Hilbert Spaces. Lecture Notes in Mathematics vol. 2057. Springer, Heidelberg (2012)","DOI":"10.1007\/978-3-642-30901-4"},{"key":"9768_CR14","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/j.jmaa.2012.04.072","volume":"394","author":"A Cegielski","year":"2012","unstructured":"Cegielski, A., Censor, Y.: Extrapolation and local acceleration of an iterative process for common fixed point problems. J. Math. Anal. Appl. 394, 809\u2013818 (2012)","journal-title":"J. Math. Anal. Appl."},{"key":"9768_CR15","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s10589-009-9233-x","volume":"47","author":"A Cegielski","year":"2010","unstructured":"Cegielski, A., Dylewski, R.: Variable target value relaxed alternating projection method. Comput. Optim. Appl. 47, 455\u2013476 (2010)","journal-title":"Comput. Optim. Appl."},{"key":"9768_CR16","first-page":"1093","volume":"19","author":"A Cegielski","year":"2008","unstructured":"Cegielski, A., Suchocka, A.: Relaxed alternating projection methods, SIAM. J. Optim. 19, 1093\u20131106 (2008)","journal-title":"J. Optim."},{"key":"9768_CR17","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.laa.2005.10.006","volume":"416","author":"Y Censor","year":"2006","unstructured":"Censor, Y.: Computational acceleration of projection algorithms for the linear best approximation problem. Linear Algebra Appl. 416, 111\u2013123 (2006)","journal-title":"Linear Algebra Appl."},{"key":"9768_CR18","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/0168-9274(87)90028-6","volume":"3","author":"Y Censor","year":"1987","unstructured":"Censor, Y., Herman, G.T.: On some optimization techniques in image reconstruction from projections. Appl. Numer. Math. 3, 365\u2013391 (1987)","journal-title":"Appl. Numer. Math."},{"key":"9768_CR19","first-page":"407","volume":"2","author":"Y Censor","year":"1998","unstructured":"Censor, Y., Reich, S.: The Dykstra\u2019s algorithm with Bregman projections. Commun. Appl. Anal. 2, 407\u2013419 (1998)","journal-title":"Commun. Appl. Anal."},{"key":"9768_CR20","volume-title":"Parallel Optimization: Theory, Algorithms, and Applications","author":"Y Censor","year":"1997","unstructured":"Censor, Y., Zenios, S.A.: Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, New York (1997)"},{"key":"9768_CR21","first-page":"1","volume":"5","author":"A Pierro De","year":"1985","unstructured":"De Pierro, A., Iusem, A.N.: A parallel projection method for finding a common point of a family of convex sets. Pesqui. Oper. 5, 1\u201320 (1985)","journal-title":"Pesqui. Oper."},{"key":"9768_CR22","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/S1570-579X(01)80013-6","volume-title":"Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications","author":"F Deutsch","year":"2001","unstructured":"Deutsch, F.: Accelerating the convergence of the method of alternating projections via a line search: a brief survey. In: Butnariu, D., Censor, Y., Reich, S. (eds.) Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, pp. 203\u2013217. Elsevier, Amsterdam (2001)"},{"key":"9768_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-9298-9","volume-title":"Best Approximation in Inner Product Spaces","author":"F Deutsch","year":"2001","unstructured":"Deutsch, F.: Best Approximation in Inner Product Spaces. Springer, New York (2001)"},{"key":"9768_CR24","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1080\/01630569408816580","volume":"15","author":"F Deutsch","year":"1994","unstructured":"Deutsch, F., Hundal, H.: The rate of convergence of Dykstra\u2019s cyclic projections algorithm: the polyhedral case. Numer. Funct. Anal. Optim. 15, 537\u2013565 (1994)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9768_CR25","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/0377-0427(87)90004-5","volume":"18","author":"LT Santos Dos","year":"1987","unstructured":"Dos Santos, L.T.: A parallel subgradient projections method for the convex feasibility problem. J. Comput. Appl. Math. 18, 307\u2013320 (1987)","journal-title":"J. Comput. Appl. Math."},{"key":"9768_CR26","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1080\/01621459.1983.10477029","volume":"78","author":"RL Dykstra","year":"1983","unstructured":"Dykstra, R.L.: An algorithm for restricted least-squares regression. J. Am. Stat. Assoc. 78, 837\u2013842 (1983)","journal-title":"J. Am. Stat. Assoc."},{"key":"9768_CR27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1590\/S1807-03022003000100001","volume":"22","author":"MG Eberle","year":"2003","unstructured":"Eberle, M.G., Maciel, M.C.: Finding the closest Toeplitz matrix. Comput. Appl. Math. 22, 1\u201318 (2003)","journal-title":"Comput. Appl. Math."},{"key":"9768_CR28","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10479-005-2456-z","volume":"138","author":"N Echebest","year":"2005","unstructured":"Echebest, N., Guardarucci, M.T., Scolnik, H., Vacchino, M.C.: An accelerated iterative method with diagonally scaled oblique projections for solving linear feasibility problems. Ann. Oper. Res. 138, 235\u2013257 (2005)","journal-title":"Ann. Oper. Res."},{"key":"9768_CR29","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1002\/(SICI)1099-1506(199611\/12)3:6<459::AID-NLA82>3.0.CO;2-S","volume":"3","author":"R Escalante","year":"1996","unstructured":"Escalante, R., Raydan, M.: Dykstra\u2019s algorithm for a constrained least-squares matrix problem. Numer. Linear Algebra Appl. 3, 459\u2013471 (1996)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9768_CR30","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/S0898-1221(98)00020-0","volume":"35","author":"R Escalante","year":"1998","unstructured":"Escalante, R., Raydan, M.: On Dykstra\u2019s algorithm for constrained least-squares rectangular matrix problems. Comput. Math. Appl. 35, 73\u201379 (1998)","journal-title":"Comput. Math. Appl."},{"key":"9768_CR31","doi-asserted-by":"crossref","DOI":"10.1137\/9781611971941","volume-title":"Alternating Projection Methods.","author":"R Escalante","year":"2011","unstructured":"Escalante, R., Raydan, M.: Alternating Projection Methods. SIAM, Philadelphia (2011)"},{"key":"9768_CR32","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9180-5","volume-title":"Projectors and Projection Methods","author":"A Gal\u00e1ntai","year":"2004","unstructured":"Gal\u00e1ntai, A.: Projectors and Projection Methods. Kluwer Academic Publishers, Dordrecht (2004)"},{"key":"9768_CR33","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1023\/A:1019192926247","volume":"21","author":"UM Garc\u00eda-Palomares","year":"1999","unstructured":"Garc\u00eda-Palomares, U.M.: Preconditioning projection methods for solving algebraic linear systems. Numer. Algorithms 21, 157\u2013164 (1999)","journal-title":"Numer. Algorithms"},{"key":"9768_CR34","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0377-0427(89)90296-3","volume":"26","author":"W Gearhart","year":"1989","unstructured":"Gearhart, W., Koshy, M.: Acceleration schemes for the method of alternating projection. J. Comput. Appl. Math. 26, 235\u2013249 (1989)","journal-title":"J. Comput. Appl. Math."},{"key":"9768_CR35","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1137\/0611042","volume":"11","author":"W Glunt","year":"1990","unstructured":"Glunt, W., Hayden, T.L., Hong, S., Wells, J.: An alternating projection algorithm for computing the nearest Euclidean distance matrix. SIAM J. Matrix Anal. Appl. 11, 589\u2013600 (1990)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9768_CR36","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1016\/0005-1098(96)00057-X","volume":"32","author":"KM Grigoriadis","year":"1996","unstructured":"Grigoriadis, K.M., Skelton, R.: Low order control design for LMI problems using alternating projection methods. Automatica 32, 1117\u20131125 (1996)","journal-title":"Automatica"},{"issue":"6","key":"9768_CR37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0041-5553(67)90113-9","volume":"7","author":"LG Gubin","year":"1967","unstructured":"Gubin, L.G., Polyak, B.T., Raik, E.V.: The method of projections for finding the common point of convex sets. USSR Comput. Math. Math. Phys. 7(6), 1\u201324 (1967)","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"9768_CR38","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1093\/imanum\/22.3.329","volume":"22","author":"N Higham","year":"2002","unstructured":"Higham, N.: Computing the nearest correlation matrix - a problem from finance, IMA. J. Numer. Anal. 22, 329\u2013343 (2002)","journal-title":"J. Numer. Anal."},{"key":"9768_CR39","first-page":"335","volume":"77","author":"H Hundal","year":"1997","unstructured":"Hundal, H., Deutsch, F.: Two generalizations of Dykstra\u2019s cyclic projections algorithm. Math. Program. 77, 335\u2013355 (1997)","journal-title":"Math. Program."},{"key":"9768_CR40","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1007\/s11075-004-5882-0","volume":"38","author":"LM Hern\u00e1ndez-Ramos","year":"2005","unstructured":"Hern\u00e1ndez-Ramos, L.M.: Alternating oblique projections for coupled linear systems. Numer. Algorithms 38, 285\u2013303 (2005)","journal-title":"Numer. Algorithms"},{"key":"9768_CR41","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.1080\/01630563.2011.591954","volume":"32","author":"LM Hern\u00e1ndez-Ramos","year":"2011","unstructured":"Hern\u00e1ndez-Ramos, L.M., Escalante, R., Raydan, M.: Unconstrained optimization techniques for the acceleration of alternating projection methods. Numer. Funct. Anal. Optim. 32, 1041\u20131066 (2011)","journal-title":"Numer. Funct. Anal. Optim."},{"key":"9768_CR42","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1007\/BF01389537","volume":"49","author":"AN Iusem","year":"1986","unstructured":"Iusem, A.N., De Pierro, A.: Convergence results for an accelerated nonlinear Cimmino algorithm. Numer. Math. 49, 367\u2013378 (1986)","journal-title":"Numer. Math."},{"issue":"8","key":"9768_CR43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0266-5611\/28\/8\/085004","volume":"28","author":"G L\u00f3pez","year":"2012","unstructured":"L\u00f3pez, G., Mart\u00edn-M\u00e1rquez, V., Wang, F., Xu, H.-K.: Solving the split feasibility problem without prior knowledge of matrix norms. Inverse Probl. 28(8), 1\u201318 (2012). doi: 10.1088\/0266-5611\/28\/8\/085004","journal-title":"Inverse Probl."},{"key":"9768_CR44","volume-title":"Optimization by Vector Space Methods","author":"DG Luenberger","year":"1969","unstructured":"Luenberger, D.G.: Optimization by Vector Space Methods. Wiley, New York (1969)"},{"key":"9768_CR45","doi-asserted-by":"crossref","first-page":"367","DOI":"10.1016\/0898-1221(88)90158-7","volume":"15","author":"JM Mart\u00ednez","year":"1988","unstructured":"Mart\u00ednez, J.M.: An accelerated successive orthogonal projection method for solving large-scale linear feasibility problems. Comput. Math. Appl. 15, 367\u2013373 (1988)","journal-title":"Comput. Math. Appl."},{"key":"9768_CR46","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1002\/(SICI)1099-1506(199811\/12)5:6<461::AID-NLA141>3.0.CO;2-V","volume":"5","author":"M Mendoza","year":"1998","unstructured":"Mendoza, M., Raydan, M., Tarazaga, P.: Computing the nearest diagonally dominant matrix. Numer. Linear Algebra Appl. 5, 461\u2013474 (1998)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9768_CR47","doi-asserted-by":"crossref","first-page":"1784","DOI":"10.1016\/j.ymssp.2008.06.011","volume":"23","author":"J Moreno","year":"2009","unstructured":"Moreno, J., Datta, B., Raydan, M.: A symmetry preserving alternating projection method for matrix model updating. Mech. Syst. Signal Process. 23, 1784\u20131791 (2009)","journal-title":"Mech. Syst. Signal Process."},{"key":"9768_CR48","doi-asserted-by":"crossref","first-page":"635","DOI":"10.1016\/j.amc.2004.06.136","volume":"167","author":"PM Morillas","year":"2005","unstructured":"Morillas, P.M.: Dykstra\u2019s algorithm with strategies for projecting onto certain polyhedral cones. Appl. Math. Comp. 167, 635\u2013649 (2005)","journal-title":"Appl. Math. Comp."},{"key":"9768_CR49","doi-asserted-by":"crossref","unstructured":"Pang, C.H.J.: Set intersection problems: supporting hyperplanes and quadratic programming. Math. Program., Ser. A, (2014). doi: 10.1007\/s10107-014-0759-z","DOI":"10.1007\/s10107-014-0759-z"},{"key":"9768_CR50","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1137\/S0036142900367557","volume":"40","author":"C Perkins","year":"2002","unstructured":"Perkins, C.: A convergence analysis of Dykstra\u2019s algorithm for polyhedral sets. SIAM J. Numer. Anal. 40, 792\u2013804 (2002)","journal-title":"SIAM J. Numer. Anal."},{"key":"9768_CR51","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1007\/BF02612715","volume":"28","author":"G Pierra","year":"1984","unstructured":"Pierra, G.: Decomposition through formalization in a product space. Math. Prog. 28, 96\u2013118 (1984)","journal-title":"Math. Prog."},{"key":"9768_CR52","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1002\/nla.277","volume":"9","author":"M Raydan","year":"2002","unstructured":"Raydan, M., Tarazaga, P.: Primal and polar approach for computing the symmetric diagonally dominant projection. Numer. Linear Algebra Appl. 9, 333\u2013345 (2002)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9768_CR53","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/s00041-008-9030-4","volume":"15","author":"T Strohmer","year":"2009","unstructured":"Strohmer, T., Vershynin, R.: A randomized Kaczmarz algorithm with exponential convergence. J. Fourier Anal. Appl. 15, 262\u2013278 (2009)","journal-title":"J. Fourier Anal. Appl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9768-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-015-9768-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-015-9768-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T10:07:17Z","timestamp":1566900437000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-015-9768-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,23]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,1]]}},"alternative-id":["9768"],"URL":"https:\/\/doi.org\/10.1007\/s10589-015-9768-y","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,23]]}}}