{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T06:05:21Z","timestamp":1763964321819,"version":"3.45.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/100017142","name":"Gruppo Nazionale per il Calcolo Scientifico","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100017142","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003407","name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["2022ANC8HL"],"award-info":[{"award-number":["2022ANC8HL"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100031060","name":"European High Performance Computing Joint Undertaking","doi-asserted-by":"publisher","award":["955701"],"award-info":[{"award-number":["955701"]}],"id":[{"id":"10.13039\/100031060","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008314","name":"Athens University of Economics and Business","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100008314","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s11075-025-02157-y","type":"journal-article","created":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T03:29:54Z","timestamp":1751945394000},"page":"1893-1927","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Blocking structures, approximation, and preconditioning"],"prefix":"10.1007","volume":"100","author":[{"given":"Nikos","family":"Barakitis","sequence":"first","affiliation":[]},{"given":"Marco","family":"Donatelli","sequence":"additional","affiliation":[]},{"given":"Samuele","family":"Ferri","sequence":"additional","affiliation":[]},{"given":"Valerio","family":"Loi","sequence":"additional","affiliation":[]},{"given":"Stefano","family":"Serra-Capizzano","sequence":"additional","affiliation":[]},{"given":"Rosita Luisa","family":"Sormani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,7,8]]},"reference":[{"issue":"2","key":"2157_CR1","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s40590-025-00719-7","volume":"31","author":"A Adriani","year":"2025","unstructured":"Adriani, A., Schiavoni-Piazza, A.J.A., Serra-Capizzano, S.: Block structures, g.a.c.s. approximation, and distributions. Bol. Soc. Mat. Mex. - special Volume in Memory of Prof. Nikolai Vasilevski 31(2), 41 (2025)","journal-title":"Bol. Soc. Mat. Mex. - special Volume in Memory of Prof. Nikolai Vasilevski"},{"key":"2157_CR2","doi-asserted-by":"crossref","unstructured":"Adriani, A., Schiavoni-Piazza, A.J.A., Serra-Capizzano, S., Tablino-Possio, C.: Revisiting the notion of approximating class of sequences for handling approximated PDEs on moving or unbounded domains. Electron. Trans. Numer. Anal., to appear (2025)","DOI":"10.1553\/etna_vol63s424"},{"key":"2157_CR3","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/BF01389448","volume":"48","author":"O Axelsson","year":"1986","unstructured":"Axelsson, O., Lindskog, G.: On the rate of convergence of the preconditioned conjugate gradient method. Numer. Math. 48, 499\u2013523 (1986)","journal-title":"Numer. Math."},{"issue":"5","key":"2157_CR4","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2441","volume":"29","author":"N Barakitis","year":"2022","unstructured":"Barakitis, N., Ekstr\u00f6m, S.-E., Vassalos, P.: Preconditioners for fractional diffusion equations based on the spectral symbol. Numer. Linear Algebra Appl. 29(5), e2441 (2022)","journal-title":"Numer. Linear Algebra Appl."},{"key":"2157_CR5","doi-asserted-by":"crossref","unstructured":"Barakitis, N., Ferrari, P., Furci, I., Serra-Capizzano, S.: An extradimensional approach for distributional results: the case of $$2\\times 2$$ block Toeplitz structures. Springer Proceedings on Mathematics and Statistics, Mathematical Modeling with Modern Applications. Springer, Cham, in press (expected August 2025)","DOI":"10.1007\/978-3-031-89041-3_4"},{"key":"2157_CR6","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1553\/etna_vol55s585","volume":"55","author":"G Barbarino","year":"2022","unstructured":"Barbarino, G., Garoni, C., Mazza, M., Serra-Capizzano, S.: Rectangular GLT sequences. Electron. Trans. Numer. Anal. 55, 585\u2013617 (2022)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"2157_CR7","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1553\/etna_vol53s28","volume":"53","author":"G Barbarino","year":"2020","unstructured":"Barbarino, G., Garoni, C., Serra-Capizzano, S.: Block generalized locally Toeplitz sequences: theory and applications in the unidimensional case. Electron. Trans. Numer. Anal. 53, 28\u2013112 (2020)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"2157_CR8","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1553\/etna_vol53s113","volume":"53","author":"G Barbarino","year":"2020","unstructured":"Barbarino, G., Garoni, C., Serra-Capizzano, S.: Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case. Electron. Trans. Numer. Anal. 53, 113\u2013216 (2020)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"2157_CR9","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1007\/s10915-023-02449-2","volume":"98","author":"P Benedusi","year":"2024","unstructured":"Benedusi, P., Ferrari, P., Rognes, M.E., Serra-Capizzano, S.: Modeling excitable cells with the EMI equations: spectral analysis and iterative solution strategy. J. Sci. Comput. 98, 58 (2024)","journal-title":"J. Sci. Comput."},{"key":"2157_CR10","doi-asserted-by":"crossref","unstructured":"Bhatia, R.: Matrix Analysis. Graduate Texts in Mathematics, Springer-Verlag, New York (1997)","DOI":"10.1007\/978-1-4612-0653-8"},{"key":"2157_CR11","doi-asserted-by":"publisher","first-page":"2151","DOI":"10.1016\/j.camwa.2014.07.020","volume":"68","author":"D Boffi","year":"2014","unstructured":"Boffi, D., Gastaldi, L., Ruggeri, M.: Mixed formulation for interface problems with distributed Lagrange multiplier. Comput. Math. Appl. 68, 2151\u20132166 (2014)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"2157_CR12","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1137\/21M1390554","volume":"43","author":"M Bolten","year":"2022","unstructured":"Bolten, M., Donatelli, M., Ferrari, P., Furci, I.: A symbol-based analysis for multigrid methods for block-circulant and block-Toeplitz systems. SIAM J. Matrix Anal. Appl. 43(1), 405\u2013438 (2022)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2157_CR13","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/j.apnum.2023.07.016","volume":"193","author":"M Bolten","year":"2023","unstructured":"Bolten, M., Donatelli, M., Ferrari, P., Furci, I.: Symbol based convergence analysis in block multigrid methods with applications for Stokes problems. Appl. Numer. Math. 193, 109\u2013130 (2023)","journal-title":"Appl. Numer. Math."},{"key":"2157_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1426-7","volume-title":"Introduction to large truncated Toeplitz matrices","author":"A B\u00f6ttcher","year":"1999","unstructured":"B\u00f6ttcher, A., Silbermann, B.: Introduction to large truncated Toeplitz matrices. Universitext, Springer-Verlag, New York (1999)"},{"key":"2157_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511618635","volume-title":"Finite elements","author":"D Braess","year":"2007","unstructured":"Braess, D.: Finite elements. Cambridge University Press, Cambridge (2007)"},{"key":"2157_CR16","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/s10444-008-9084-5","volume":"31","author":"JF Cai","year":"2009","unstructured":"Cai, J.F., Chan, R.H., Shen, L., Shen, Z.: Convergence analysis of tight framelet approach for missing data recovery. Adv. Comput. Math. 31, 87\u2013113 (2009)","journal-title":"Adv. Comput. Math."},{"key":"2157_CR17","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.acha.2007.10.002","volume":"24","author":"JF Cai","year":"2008","unstructured":"Cai, J.F., Chan, R.H., Shen, Z.: A framelet-based image inpainting algorithm. Appl. Comput. Harmon. Anal. 24, 131\u2013149 (2008)","journal-title":"Appl. Comput. Harmon. Anal."},{"issue":"3","key":"2157_CR18","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1137\/S0036144594276474","volume":"38","author":"RH Chan","year":"1996","unstructured":"Chan, R.H., Ng, M.K.: Conjugate gradient methods for Toeplitz systems. SIAM Rev. 38(3), 427\u2013482 (1996)","journal-title":"SIAM Rev."},{"issue":"4","key":"2157_CR19","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1137\/0909051","volume":"9","author":"TF Chan","year":"1988","unstructured":"Chan, T.F.: An optimal Circulant preconditioner for Toeplitz systems. SIAM J. Sci. Statist. Comput. 9(4), 766\u2013771 (1988)","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"2157_CR20","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1016\/j.cam.2013.05.018","volume":"272","author":"V Del Prete","year":"2014","unstructured":"Del Prete, V., Di Benedetto, F., Donatelli, M., Serra-Capizzano, S.: Symbol approach in a signal-restoration problem involving block Toeplitz matrices. J. Comput. Appl. Math. 272, 399\u2013416 (2014)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"2157_CR21","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1080\/03081080008818658","volume":"48","author":"F Di Benedetto","year":"2000","unstructured":"Di Benedetto, F., Serra-Capizzano, S.: Optimal multilevel matrix algebra operators. Linear Multilinear Algebra 48(1), 35\u201366 (2000)","journal-title":"Linear Multilinear Algebra"},{"issue":"5","key":"2157_CR22","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1016\/j.camwa.2017.05.024","volume":"74","author":"M Donatelli","year":"2017","unstructured":"Donatelli, M., Dorostkar, A., Mazza, M., Neytcheva, M., Serra-Capizzano, S.: Function-based block multigrid strategy for a two-dimensional linear elasticity-type problem. Comput. Math. Appl. 74(5), 1015\u20131028 (2017)","journal-title":"Comput. Math. Appl."},{"issue":"4","key":"2157_CR23","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2356","volume":"28","author":"M Donatelli","year":"2021","unstructured":"Donatelli, M., Ferrari, P., Furci, I., Serra-Capizzano, S., Sesana, D.: Multigrid methods for block-Toeplitz linear systems: convergence analysis and applications. Numer. Linear Algebra Appl. 28(4), e2356 (2021)","journal-title":"Numer. Linear Algebra Appl."},{"key":"2157_CR24","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1016\/j.jcp.2015.11.061","volume":"307","author":"M Donatelli","year":"2016","unstructured":"Donatelli, M., Mazza, M., Serra-Capizzano, S.: Spectral analysis and structure preserving preconditioners for fractional diffusion equations. J. Comput. Phys. 307, 262\u2013279 (2016)","journal-title":"J. Comput. Phys."},{"key":"2157_CR25","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.cma.2016.05.042","volume":"309","author":"A Dorostkar","year":"2016","unstructured":"Dorostkar, A., Neytcheva, M., Serra-Capizzano, S.: Spectral analysis of coupled PDEs and of their Schur complements via Generalized Locally Toeplitz sequences in 2D. Comput. Methods Appl. Mech. Engrg. 309, 74\u2013105 (2016)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"5","key":"2157_CR26","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2151","volume":"25","author":"M Dumbser","year":"2018","unstructured":"Dumbser, M., Fambri, F., Furci, I., Mazza, M., Serra-Capizzano, S., Tavelli, M.: Staggered discontinuous Galerkin methods for the incompressible Navier-Stokes equations: spectral analysis and computational results. Numer. Linear Algebra Appl. 25(5), e2151 (2018)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"1\u20133","key":"2157_CR27","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0024-3795(99)00251-7","volume":"306","author":"D Fasino","year":"2000","unstructured":"Fasino, D., Tilli, P.: Spectral clustering properties of block multilevel Hankel matrices. Linear Algebra Appl. 306(1\u20133), 155\u2013163 (2000)","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"2157_CR28","doi-asserted-by":"publisher","first-page":"5","DOI":"10.3390\/math8010005","volume":"8","author":"P Ferrari","year":"2020","unstructured":"Ferrari, P., Rahla, R.I., Tablino-Possio, C., Belhaj, S., Serra-Capizzano, S.: Multigrid for $$\\mathbb{Q} _{k}$$ finite element matrices using a (block) Toeplitz symbol approach. Mathematics 8(1), 5 (2020)","journal-title":"Mathematics"},{"key":"2157_CR29","unstructured":"Furci, I., Adriani, A., Serra-Capizzano, S.: Block structured matrix-sequences and their spectral and singular value canonical distributions: a general theory. Arxiv.org:2409.06465 (2024)"},{"key":"2157_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-53679-8","volume-title":"Generalized Locally Toeplitz sequences: theory and applications","author":"C Garoni","year":"2017","unstructured":"Garoni, C., Serra-Capizzano, S.: Generalized Locally Toeplitz sequences: theory and applications, vol. I. Springer, Cham (2017)"},{"key":"2157_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-02233-4","volume-title":"Generalized Locally Toeplitz sequences: theory and applications","author":"C Garoni","year":"2018","unstructured":"Garoni, C., Serra-Capizzano, S.: Generalized Locally Toeplitz sequences: theory and applications, vol. II. Springer, Cham (2018)"},{"key":"2157_CR32","doi-asserted-by":"publisher","first-page":"1100","DOI":"10.1137\/140976480","volume":"36","author":"C Garoni","year":"2015","unstructured":"Garoni, C., Serra-Capizzano, S., Sesana, D.: Spectral analysis and spectral symbol of $$d$$-variate $$\\mathbb{Q} _p$$ Lagrangian FEM stiffness matrices. SIAM J. Matrix Anal. Appl. 36, 1100\u20131128 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"5","key":"2157_CR33","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1007\/s11831-018-9295-y","volume":"26","author":"C Garoni","year":"2019","unstructured":"Garoni, C., Speleers, H., Ekstr\u00f6m, S.-E., Reali, A., Serra-Capizzano, S., Hughes, T.J.R.: Symbol-based analysis of finite element and isogeometric B-spline discretizations of eigenvalue problems: exposition and review. Arch. Comput. Methods Eng. 26(5), 1639\u20131690 (2019)","journal-title":"Arch. Comput. Methods Eng."},{"key":"2157_CR34","volume-title":"Toeplitz forms and their applications","author":"U Grenander","year":"1984","unstructured":"Grenander, U., Szeg\u00f6, G.: Toeplitz forms and their applications, 2nd edn. Chelsea Publishing Co., New York (1984)","edition":"2"},{"issue":"1","key":"2157_CR35","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1137\/070702564","volume":"31","author":"TK Huckle","year":"2008","unstructured":"Huckle, T.K.: Compact Fourier analysis for designing multigrid methods. SIAM J. Sci. Comput. 31(1), 644\u2013666 (2008)","journal-title":"SIAM J. Sci. Comput."},{"issue":"317","key":"2157_CR36","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1090\/mcom\/3366","volume":"88","author":"M Mazza","year":"2019","unstructured":"Mazza, M., Ratnani, A., Serra-Capizzano, S.: Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions. Math. Comp. 88(317), 1155\u20131188 (2019)","journal-title":"Math. Comp."},{"key":"2157_CR37","doi-asserted-by":"publisher","first-page":"992","DOI":"10.1016\/j.jcp.2017.08.064","volume":"350","author":"H Moghaderi","year":"2017","unstructured":"Moghaderi, H., Dehghan, M., Donatelli, M., Mazza, M.: Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations. J. Comput. Phys. 350, 992\u20131011 (2017)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"2157_CR38","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1016\/0898-1221(93)90035-T","volume":"26","author":"S Serra-Capizzano","year":"1993","unstructured":"Serra-Capizzano, S.: Multi-iterative methods. Comput. Math. Appl. 26(4), 65\u201387 (1993)","journal-title":"Comput. Math. Appl."},{"issue":"2","key":"2157_CR39","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1137\/S0895479897316904","volume":"20","author":"S Serra-Capizzano","year":"1999","unstructured":"Serra-Capizzano, S.: Toeplitz preconditioners constructed from linear approximation processes. SIAM J. Matrix Anal. Appl. 20(2), 446\u2013465 (1999)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2157_CR40","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/s002110050413","volume":"82","author":"S Serra-Capizzano","year":"1999","unstructured":"Serra-Capizzano, S.: A Korovkin-type theory for finite Toeplitz operators via matrix algebras. Numer. Math. 82, 117\u2013142 (1999)","journal-title":"Numer. Math."},{"issue":"1\u20133","key":"2157_CR41","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0024-3795(01)00335-4","volume":"337","author":"S Serra-Capizzano","year":"2001","unstructured":"Serra-Capizzano, S.: Spectral behavior of matrix sequences and discretized boundary value problems. Linear Algebra Appl. 337(1\u20133), 37\u201378 (2001)","journal-title":"Linear Algebra Appl."},{"key":"2157_CR42","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/S0024-3795(01)00361-5","volume":"343\u2013344","author":"S Serra-Capizzano","year":"2002","unstructured":"Serra-Capizzano, S.: Matrix algebra preconditioners for multilevel Toeplitz matrices are not superlinear. Linear Algebra Appl. 343\u2013344, 303\u2013319 (2002)","journal-title":"Linear Algebra Appl."},{"issue":"2\u20133","key":"2157_CR43","first-page":"557","volume":"315","author":"S Serra-Capizzano","year":"2004","unstructured":"Serra-Capizzano, S., Noutsos, D., Vassalos, P.: Matrix algebra preconditioners for multilevel Toeplitz systems do not insure optimal convergence rate. Theoret. Comput. Sci. 315(2\u20133), 557\u2013579 (2004)","journal-title":"Theoret. Comput. Sci."},{"issue":"1\u20132","key":"2157_CR44","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0377-0427(99)00104-1","volume":"108","author":"S Serra-Capizzano","year":"1999","unstructured":"Serra-Capizzano, S., Tilli, P.: Extreme singular values and eigenvalues of non-Hermitian block Toeplitz matrices. J. Comput. Appl. Math. 108(1\u20132), 113\u2013130 (1999)","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"2157_CR45","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1155\/S1025583402000152","volume":"7","author":"S Serra-Capizzano","year":"2002","unstructured":"Serra-Capizzano, S., Tilli, P.: On unitarily invariant norms of matrix-valued linear positive operators. J. Inequal. Appl. 7(3), 309\u2013330 (2002)","journal-title":"J. Inequal. Appl."},{"issue":"2\u20133","key":"2157_CR46","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1080\/03081089808818584","volume":"45","author":"P Tilli","year":"1998","unstructured":"Tilli, P.: A note on the spectral distribution of Toeplitz matrices. Linear Multilinear Algebra 45(2\u20133), 147\u2013159 (1998)","journal-title":"Linear Multilinear Algebra"},{"issue":"1\u20133","key":"2157_CR47","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1016\/S0024-3795(97)80001-8","volume":"270","author":"E Tyrtyshnikov","year":"1998","unstructured":"Tyrtyshnikov, E., Zamarashkin, N.: Spectra of multilevel Toeplitz matrices: advanced theory via simple matrix relationships. Linear Algebra Appl. 270(1\u20133), 15\u201327 (1998)","journal-title":"Linear Algebra Appl."},{"key":"2157_CR48","doi-asserted-by":"crossref","unstructured":"Van der Vorst, H.A.: Iterative Krylov Methods for Large Linear Systems. Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press (2003)","DOI":"10.1017\/CBO9780511615115"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02157-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-025-02157-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-025-02157-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T06:04:09Z","timestamp":1763964249000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-025-02157-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,8]]},"references-count":48,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["2157"],"URL":"https:\/\/doi.org\/10.1007\/s11075-025-02157-y","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2025,7,8]]},"assertion":[{"value":"29 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2025","order":3,"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 competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}