{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T21:16:29Z","timestamp":1767906989297,"version":"3.49.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T00:00:00Z","timestamp":1765238400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T00:00:00Z","timestamp":1765238400000},"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":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1007\/s12190-025-02684-w","type":"journal-article","created":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T11:53:45Z","timestamp":1765281225000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Accelerated Kaczmarz methods via randomized sketch techniques for solving consistent linear systems"],"prefix":"10.1007","volume":"72","author":[{"given":"Haochen","family":"Jiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5621-2975","authenticated-orcid":false,"given":"Dongdong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianping","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xu","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,9]]},"reference":[{"key":"2684_CR1","unstructured":"Kaczmarz, S.: Angen\u00e4emrte Aufl\u00f6sung von systemen linearer Gleichungen. Bulletin International de l\u2019Acad\u00e9mie Polonaise des Sciences et des Lettres 335\u2013337 (1937)"},{"issue":"6","key":"2684_CR2","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1016\/j.matcom.2004.01.021","volume":"65","author":"C. Popa","year":"2004","unstructured":"Popa, C., Zdunek, R.: Kaczmarz extended algorithm for tomographic image reconstruction from limited-data. Math. Comput. Simul. 65(6), 579\u2013598 (2004)","journal-title":"Math. Comput. Simul."},{"issue":"6","key":"2684_CR3","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1088\/0967-3334\/34\/6\/595","volume":"34","author":"T. Li","year":"2013","unstructured":"Li, T., Kao, T.J., Isaacson, D., Newell, J., Saulnier, G.: Adaptive Kaczmarz method for image reconstruction in electrical impedance tomography. Physiol. Meas. 34(6), 595 (2013)","journal-title":"Physiol. Meas."},{"key":"2684_CR4","doi-asserted-by":"crossref","unstructured":"Kamath, G., Ramanan, P., Song, W.Z.: Distributed randomized Kaczmarz and applications to seismic imaging in sensor network, 2015. In: International Conference on Distributed Computing in Sensor Systems, pp. 169\u2013178. Institute of Electrical and Electronics Engineers (2015)","DOI":"10.1109\/DCOSS.2015.27"},{"key":"2684_CR5","doi-asserted-by":"crossref","unstructured":"Hu, T., Liu, D., Vong, S.W.: Solving third-order tensor linear complementarity problems via modulus-based methods and applications. Numer. Algoritms. 2025, 1\u201329","DOI":"10.1007\/s11075-025-02030-y"},{"key":"2684_CR6","first-page":"246","volume":"9148","author":"R. Ramlau","year":"2014","unstructured":"Ramlau, R., Saxenhuber, D., Yudytskiy, M.: Iterative reconstruction methods in atmospheric tomography: FEWHA, Kaczmarz and gradient-based algorithm, adaptive optics systems iv. Int. Soc. Optical Eng. 9148, 246\u2013260 (2014)","journal-title":"Int. Soc. Optical Eng."},{"issue":"8\u20139","key":"2684_CR7","doi-asserted-by":"publisher","first-page":"2247","DOI":"10.1016\/j.laa.2008.06.024","volume":"429","author":"C. Popa","year":"2008","unstructured":"Popa, C.: Constrained Kaczmarz extended algorithm for image reconstruction. Linear Algebra Appl. 429(8\u20139), 2247\u20132267 (2008)","journal-title":"Linear Algebra Appl."},{"key":"2684_CR8","doi-asserted-by":"crossref","unstructured":"Lorenz, D.A., Wenger, S., Sch\u00f6pfer, F., Magnor, M.: A sparse Kaczmarz solver and a linearized Bregman method for online compressed sensing, 2014 IEEE international conference on image processing (ICIP). Inst. Electr. Electron. Eng. 1347\u20131351 (2014)","DOI":"10.1109\/ICIP.2014.7025269"},{"issue":"3","key":"2684_CR9","doi-asserted-by":"publisher","first-page":"SH61","DOI":"10.1190\/INT-2016-0001.1","volume":"4","author":"M. Abdelazeem","year":"2016","unstructured":"Abdelazeem, M., Gobashy, M.M.: A solution to unexploded ordnance detection problem from its magnetic anomaly using Kaczmarz regularization. Interpretation 4(3), SH61\u2013SH69 (2016)","journal-title":"Interpretation"},{"key":"2684_CR10","doi-asserted-by":"crossref","unstructured":"Wang, Y., Zhu, L., Xu, W.: New perturbation analysis of generalized singular values of Grassmann matrix pairs with arbitrary per mutation. J. Educ. Chang. Inf. Comput. Sci., accepted, (2025)","DOI":"10.4208\/JICS-2024-002"},{"issue":"6","key":"2684_CR11","doi-asserted-by":"publisher","first-page":"1564","DOI":"10.3390\/s20061564","volume":"20","author":"H. Wu","year":"2020","unstructured":"Wu, H., Shen, B., Zhao, S., Gong, P.: Low-complexity soft-output signal detection based on improved Kaczmarz iteration algorithm for uplink massive mimo system. Sensors 20(6), 1564 (2020)","journal-title":"Sensors"},{"issue":"1","key":"2684_CR12","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1088\/0266-5611\/20\/1\/006","volume":"20","author":"C. Byrne","year":"2003","unstructured":"Byrne, C.: A unified treatment of some iterative algorithms in signal processing and image reconstruction. Inverse Probl. 20(1), 103 (2003)","journal-title":"Inverse Probl."},{"issue":"5\u20136","key":"2684_CR13","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.parco.2009.12.003","volume":"36","author":"J.M. Elble","year":"2010","unstructured":"Elble, J.M., Sahinidis, N.V., Vouzis, P.: Gpu computing with Kaczmarzs and other iterative algorithms for linear systems. Parallel Comput. 36(5\u20136), 215\u2013231 (2010)","journal-title":"Parallel Comput."},{"issue":"5","key":"2684_CR14","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1016\/j.automatica.2012.02.025","volume":"48","author":"F. Pasqualetti","year":"2012","unstructured":"Pasqualetti, F., Carli, R., Bullo, F.: Distributed estimation via iterative projections with application to power network monitoring. Automatica 48(5), 747\u2013758 (2012)","journal-title":"Automatica"},{"key":"2684_CR15","first-page":"64","volume":"5","author":"\u00c9.D. Aved\u2019yan","year":"1978","unstructured":"Aved\u2019yan, \u00c9.D.: Modified Kaczmarz algorithms for estimating the parameters of linear plants. Avtom. Telemekh. 5, 64\u201372 (1978)","journal-title":"Avtom. Telemekh."},{"issue":"2","key":"2684_CR16","doi-asserted-by":"publisher","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(2), 262\u2013278 (2009)","journal-title":"J. Fourier Anal. Appl."},{"issue":"1","key":"2684_CR17","doi-asserted-by":"publisher","first-page":"A592","DOI":"10.1137\/17M1137747","volume":"40","author":"Z.Z. Bai","year":"2018","unstructured":"Bai, Z.Z., Wu, W.T.: On greedy randomized Kaczmarz method for solving large sparse linear systems. SIAM J. On Sci. Comput. 40(1), A592\u2013A606 (2018)","journal-title":"SIAM J. On Sci. Comput."},{"key":"2684_CR18","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.aml.2018.12.022","volume":"91","author":"J.J. Zhang","year":"2019","unstructured":"Zhang, J.J.: A new greedy Kaczmarz algorithm for the solution of very large linear systems. Appl. Math. Lett. 91, 207\u2013212 (2019)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"2684_CR19","doi-asserted-by":"publisher","first-page":"e2237","DOI":"10.1002\/nla.2237","volume":"26","author":"Z.Z. Bai","year":"2019","unstructured":"Bai, Z.Z., Wu, W.T.: On greedy randomized coordinate descent methods for solving large linear least-squares problems. Numer. Linear. Algebra. Appl. 26(4), e2237 (2019)","journal-title":"Numer. Linear. Algebra. Appl."},{"key":"2684_CR20","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1016\/j.apnum.2020.06.014","volume":"157","author":"J. Zhang","year":"2020","unstructured":"Zhang, J., Guo, J.: On relaxed greedy randomized coordinate descent methods for solving large linear least-squares problems. Appl. Numer. Math. 157, 372\u2013384 (2020)","journal-title":"Appl. Numer. Math."},{"key":"2684_CR21","doi-asserted-by":"publisher","first-page":"106294","DOI":"10.1016\/j.aml.2020.106294","volume":"104","author":"Y.Q. Niu","year":"2020","unstructured":"Niu, Y.Q., Zheng, B.: A greedy block Kaczmarz algorithm for solving large-scale linear systems. Appl. Math. Lett. 104, 106294 (2020)","journal-title":"Appl. Math. Lett."},{"key":"2684_CR22","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.aml.2018.03.008","volume":"83","author":"Z.Z. Bai","year":"2018","unstructured":"Bai, Z.Z., Wu, W.T.: On relaxed greedy randomized Kaczmarz methods for solving large sparse linear systems. Appl. Math. Lett. 83, 21\u201326 (2018)","journal-title":"Appl. Math. Lett."},{"key":"2684_CR23","doi-asserted-by":"crossref","unstructured":"Du, K., Gao, H.: A new theoretical estimate for the convergence rate of the maximal weighted residual Kaczmarz algorithm. Numer. Math.: Theory, Methods Appl. 12(2) (2019)","DOI":"10.4208\/nmtma.OA-2018-0039"},{"key":"2684_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01396365","volume":"35","author":"T. Elfving","year":"1980","unstructured":"Elfving, T.: Block-iterative methods for consistent and inconsistent linear equations. Numer. Math. 35, 1\u201312 (1980)","journal-title":"Numer. Math."},{"key":"2684_CR25","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/j.laa.2012.12.022","volume":"441","author":"D. Needell","year":"2014","unstructured":"Needell, D., Tropp, J.A.: Paved with good intentions: analysis of a randomized block Kaczmarz method. Linear. Algebra Appl. 441, 199\u2013221 (2014)","journal-title":"Linear Algebra Appl."},{"key":"2684_CR26","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.laa.2021.01.024","volume":"616","author":"Y. Liu","year":"2021","unstructured":"Liu, Y., Gu, C.Q.: On greedy randomized block Kaczmarz method for consistent linear systems. Linear. Algebra Appl. 616, 178\u2013200 (2021)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"2684_CR27","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1137\/120889897","volume":"34","author":"A. Zouzias","year":"2013","unstructured":"Zouzias, A., Freris, N.M.: Randomized extended Kaczmarz for solving least squares. SIAM J. Matrix Anal. Appl. 34(2), 773\u2013793 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2684_CR28","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1016\/j.laa.2015.06.027","volume":"484","author":"D. Needell","year":"2015","unstructured":"Needell, D., Zhao, R., Zouzias, A.: Randomized block Kaczmarz method with projection for solving least squares. Linear Algebra Appl. 484, 322\u2013343 (2015)","journal-title":"Linear Algebra Appl."},{"key":"2684_CR29","doi-asserted-by":"publisher","first-page":"124907","DOI":"10.1016\/j.amc.2019.124907","volume":"370","author":"J.Q. Chen","year":"2020","unstructured":"Chen, J.Q., Huang, Z.D.: On the error estimate of the randomized double block Kaczmarz method. Appl. Math. Computation 370, 124907 (2020)","journal-title":"Appl. Math. Computation"},{"key":"2684_CR30","doi-asserted-by":"publisher","first-page":"113828","DOI":"10.1016\/j.cam.2021.113828","volume":"403","author":"X.L. Jiang","year":"2022","unstructured":"Jiang, X.L., Zhang, K., Yin, J.F.: Randomized block Kaczmarz methods with k-means clustering for solving large linear systems. J. Comput. Appl. Math. 403, 113828 (2022)","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"2684_CR31","doi-asserted-by":"publisher","first-page":"1425","DOI":"10.1137\/19M1251643","volume":"40","author":"I. Necoara","year":"2019","unstructured":"Necoara, I.: Faster randomized block Kaczmarz algorithms. SIAM J. Matrix Anal. Appl. 40(4), 1425\u20131452 (2019)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2684_CR32","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1016\/j.apnum.2024.04.016","volume":"202","author":"Y. Liao","year":"2024","unstructured":"Liao, Y., Li, W., Yang, D.: The accelerated tensor Kaczmarz algorithm with adaptive parameters for solving tensor systems. Appl. Numer. Math. 202, 100\u2013119 (2024)","journal-title":"Appl. Numer. Math."},{"key":"2684_CR33","doi-asserted-by":"publisher","first-page":"126486","DOI":"10.1016\/j.amc.2021.126486","volume":"410","author":"Y. Zhang","year":"2021","unstructured":"Zhang, Y., Li, H.: A count sketch maximal weighted residual Kaczmarz method for solving highly overdetermined linear systems. Appl. Math. And Computation 410, 126486 (2021)","journal-title":"Appl. Math. And Computation"},{"issue":"4","key":"2684_CR34","doi-asserted-by":"publisher","first-page":"260","DOI":"10.4236\/apm.2022.124020","volume":"12","author":"P. Zhang","year":"2022","unstructured":"Zhang, P., Li, L., Zhang, P.: A count sketch maximal weighted residual Kaczmarz method with oblique projection for highly overdetermined linear systems. Adv. Pure Math. 12(4), 260\u2013270 (2022)","journal-title":"Adv. Pure Math."},{"key":"2684_CR35","doi-asserted-by":"crossref","unstructured":"Meng, X., Mahoney, M.W.: Low-distortion subspace embeddings in input-sparsity time and applications to robust linear regression. In: Proceedings of the forty-fifth annual ACM symposium on Theory of computing, pp. 91\u2013100. (2013)","DOI":"10.1145\/2488608.2488621"},{"issue":"1\u20132","key":"2684_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0400000060","volume":"10","author":"D.P. Woodruff","year":"2014","unstructured":"Woodruff, D.P.: Sketching as a tool for numerical linear algebra. Found. Trends Theor. Comput. Sci. 10(1\u20132), 1\u2013157 (2014)","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"2684_CR37","unstructured":"Wang, S.: A practical guide to randomized matrix computations with MATLAB implementations. arXiv preprint arXiv:1505.07570, (2015)"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02684-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-025-02684-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02684-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T16:47:13Z","timestamp":1767890833000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-025-02684-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,9]]},"references-count":37,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["2684"],"URL":"https:\/\/doi.org\/10.1007\/s12190-025-02684-w","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,9]]},"assertion":[{"value":"31 May 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 September 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2025","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 that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"48"}}