{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:32:25Z","timestamp":1758814345923,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T00:00:00Z","timestamp":1591574400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T00:00:00Z","timestamp":1591574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Russian Foundation for Basic Research","award":["17-01-00854"],"award-info":[{"award-number":["17-01-00854"]}]},{"name":"Russian Foundation for Basic Research","award":["16-31-60095"],"award-info":[{"award-number":["16-31-60095"]}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"crossref","award":["15-11-00033"],"award-info":[{"award-number":["15-11-00033"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1007\/s10444-020-09794-y","type":"journal-article","created":{"date-parts":[[2020,6,8]],"date-time":"2020-06-08T09:05:56Z","timestamp":1591607156000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Simple non-extensive sparsification of the hierarchical matrices"],"prefix":"10.1007","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5903-6417","authenticated-orcid":false,"given":"Daria A.","family":"Sushnikova","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivan V.","family":"Oseledets","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,6,8]]},"reference":[{"issue":"3","key":"9794_CR1","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1007\/s10915-013-9714-z","volume":"57","author":"S Ambikasaran","year":"2013","unstructured":"Ambikasaran, S., Darve, E.: An ${\\mathscr{O}}(n\\log n)$ fast direct solver for partial hierarchically semi-separable matrices. J. Sci. Comput. 57 (3), 477\u2013501 (2013)","journal-title":"J. Sci. Comput."},{"unstructured":"Ambikasaran, S., Darve, E.: The inverse fast multipole method. arXiv:1309.1773 (2014)","key":"9794_CR2"},{"issue":"2","key":"9794_CR3","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1109\/TPAMI.2015.2448083","volume":"38","author":"S Ambikasaran","year":"2016","unstructured":"Ambikasaran, S., Foreman-Mackey, D., Greengard, L., Hogg, D. W., O\u2019Neil, M.: Fast direct methods for gaussian processes. IEEE T Pattern Anal. 38 (2), 252\u2013265 (2016)","journal-title":"IEEE T Pattern Anal."},{"issue":"3","key":"9794_CR4","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s00607-004-0099-6","volume":"74","author":"M Bebendorf","year":"2005","unstructured":"Bebendorf, M.: Hierarchical LU decomposition-based preconditioners for BEM. Computing 74(3), 225\u2013247 (2005)","journal-title":"Computing"},{"unstructured":"B\u00f6rm, S.: ${\\mathscr{H}}$2lib package. http:\/\/www.h2lib.org\/","key":"9794_CR5"},{"doi-asserted-by":"crossref","unstructured":"B\u00f6rm, S.: Efficient numerical methods for non-local operators: ${\\mathscr{H}}^{2}$-matrix compression, algorithms and analysis, vol. 14. European Mathematical Society (2010)","key":"9794_CR6","DOI":"10.4171\/091"},{"doi-asserted-by":"crossref","unstructured":"B\u00f6rm, S.: ${\\mathscr{H}}^{2}$-matrix compression. In: New Developments in the Visualization and Processing of Tensor Fields, pp. 339\u2013362. Springer (2012)","key":"9794_CR7","DOI":"10.1007\/978-3-642-27343-8_18"},{"issue":"5","key":"9794_CR8","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1016\/S0955-7997(02)00152-2","volume":"27","author":"S B\u00f6rm","year":"2003","unstructured":"B\u00f6rm, S., Grasedyck, L., Hackbusch, W.: Introduction to hierarchical matrices with applications. Eng. Anal. Bound. Elem. 27(5), 405\u2013422 (2003). https:\/\/doi.org\/10.1016\/S0955-7997(02)00152-2","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"6","key":"9794_CR9","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s00791-015-0233-3","volume":"16","author":"S B\u00f6rm","year":"2013","unstructured":"B\u00f6rm, S., Reimer, K.: Efficient arithmetic operations for rank-structured matrices based on hierarchical low-rank updates. Comput. Vis. Sci. 16(6), 247\u2013258 (2013)","journal-title":"Comput. Vis. Sci."},{"issue":"1","key":"9794_CR10","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1137\/050639028","volume":"29","author":"S Chandrasekaran","year":"2006","unstructured":"Chandrasekaran, S., Dewilde, P., Gu, M., Lyons, W., Pals, T.: A fast solver for HSS representations via sparse matrices. SIAM J. Matrix Anal. A. 29(1), 67\u201381 (2006)","journal-title":"SIAM J. Matrix Anal. A."},{"unstructured":"Coulier, P., Pouransari, H., Darve, E.: The inverse fast multipole method: using a fast approximate direct solver as a preconditioner for dense linear systems. arXiv:1508.01835 (2015)","key":"9794_CR11"},{"issue":"4","key":"9794_CR12","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1145\/1462173.1462176","volume":"35","author":"TA Davis","year":"2009","unstructured":"Davis, T. A., Hager, W. W.: Dynamic supernodes in sparse Cholesky update\/downdate and triangular solves. ACM T Math. Softw. 35(4), 27 (2009)","journal-title":"ACM T Math. Softw."},{"issue":"2","key":"9794_CR13","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0021-9991(87)90140-9","volume":"73","author":"L Greengard","year":"1987","unstructured":"Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73(2), 325\u2013348 (1987)","journal-title":"J. Comput. Phys."},{"doi-asserted-by":"crossref","unstructured":"Greengard, L., Rokhlin, V.: The Rapid Evaluation of Potential Fields in Three Dimensions. Springer, Berlin (1988)","key":"9794_CR14","DOI":"10.7551\/mitpress\/5750.001.0001"},{"issue":"2","key":"9794_CR15","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s006070050015","volume":"62","author":"W Hackbusch","year":"1999","unstructured":"Hackbusch, W.: A sparse matrix arithmetic based on ${\\mathscr{H}}$-matrices. Part I: introduction to ${\\mathscr{H}}$-matrices. Computing 62(2), 89\u2013108 (1999)","journal-title":"Computing"},{"doi-asserted-by":"crossref","unstructured":"Hackbusch, W., Khoromskij, B., Sauter, S.: On ${\\mathscr{H}}^{2}$-Matrices. In: Bungartz, H.-J. et al. (eds.) Lectures on Applied Mathematics, pp 9\u201330. Springer, Berlin (2000)","key":"9794_CR16","DOI":"10.1007\/978-3-642-59709-1_2"},{"issue":"1","key":"9794_CR17","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/PL00021408","volume":"64","author":"W Hackbusch","year":"2000","unstructured":"Hackbusch, W., Khoromskij, B. N.: A sparse h-matrix arithmetic. Computing 64(1), 21\u201347 (2000)","journal-title":"Computing"},{"issue":"3","key":"9794_CR18","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00607-004-0080-4","volume":"73","author":"W Hackbusch","year":"2004","unstructured":"Hackbusch, W., Khoromskij, B. N., Kriemann, R.: Hierarchical matrices based on a weak admissibility criterion. Computing 73(3), 207\u2013243 (2004)","journal-title":"Computing"},{"doi-asserted-by":"crossref","unstructured":"Ma, M., Jiao, D.: Accuracy directly controlled fast direct solutions of general ${\\mathscr{H}},^{2}$-matrices and its application to electrically large integral-equation-based electromagnetic analysis. arXiv:1703.06155 (2017)","key":"9794_CR19","DOI":"10.1109\/ICEAA.2017.8065612"},{"issue":"4","key":"9794_CR20","doi-asserted-by":"crossref","first-page":"1251","DOI":"10.1137\/100786617","volume":"32","author":"PG Martinsson","year":"2011","unstructured":"Martinsson, P. G.: A fast randomized algorithm for computing a hierarchically semiseparable representation of a matrix. SIAM J. Matrix Anal. A. 32(4), 1251\u20131274 (2011)","journal-title":"SIAM J. Matrix Anal. A."},{"issue":"1","key":"9794_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2004.10.033","volume":"205","author":"PG Martinsson","year":"2005","unstructured":"Martinsson, P. G., Rokhlin, V.: A fast direct solver for boundary integral equations in two dimensions. J. Comput. Phys. 205(1), 1\u201323 (2005)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9794_CR22","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1002\/nla.2021","volume":"23","author":"AY Mikhalev","year":"2016","unstructured":"Mikhalev, A. Y., Oseledets, I. V.: Iterative representing set selection for nested cross approximation. Numer. Linear Algebra Appl. 23(2), 230\u2013248 (2016)","journal-title":"Numer. Linear Algebra Appl."},{"issue":"2","key":"9794_CR23","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1137\/16M1095949","volume":"15","author":"V Minden","year":"2017","unstructured":"Minden, V., Ho, K. L., Damle, A., Ying, L.: A recursive skeletonization factorization based on strong admissibility. Multiscale Model. Simul. 15(2), 768\u2013796 (2017)","journal-title":"Multiscale Model. Simul."},{"doi-asserted-by":"crossref","unstructured":"Sheng, Z., Dewilde, P., Chandrasekaran, S.: Algorithms to solve hierarchically semi-separable systems. In: System Theory, the Schur Algorithm and Multidimensional Analysis, pp. 255\u2013294. Springer (2007)","key":"9794_CR24","DOI":"10.1007\/978-3-7643-8137-0_5"},{"doi-asserted-by":"crossref","unstructured":"Solovyev, S.: Multifrontal hierarchically solver for 3D discretized elliptic equations. In: International Conference on Finite Difference Methods, pp. 371\u2013378. Springer (2014)","key":"9794_CR25","DOI":"10.1007\/978-3-319-20239-6_41"},{"unstructured":"Sushnikova, D. A., Oseledets, I.V.: \u201cCompress and eliminate\u201d solver for symmetric positive definite sparse matrices. arXiv:1603.09133(2016)","key":"9794_CR26"},{"issue":"1","key":"9794_CR27","first-page":"29","volume":"31","author":"DA Sushnikova","year":"2016","unstructured":"Sushnikova, D. A., Oseledets, I. V.: Preconditioners for hierarchical matrices based on their extended sparse form. Russ. J. Numer. Anal. M. 31(1), 29\u201340 (2016)","journal-title":"Russ. J. Numer. Anal. M."},{"issue":"1","key":"9794_CR28","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/BF02575706","volume":"33","author":"EE Tyrtyshnikov","year":"1996","unstructured":"Tyrtyshnikov, E. E.: Mosaic-skeleton approximations. Calcolo 33(1), 47\u201357 (1996). https:\/\/doi.org\/10.1007\/BF02575706","journal-title":"Calcolo"},{"issue":"3","key":"9794_CR29","doi-asserted-by":"crossref","first-page":"1382","DOI":"10.1137\/09074543X","volume":"31","author":"J Xia","year":"2009","unstructured":"Xia, J., Chandrasekaran, S., Gu, M., Li, X. S.: Superfast multifrontal method for large structured linear systems of equations. SIAM J. Matrix Anal. A. 31(3), 1382\u20131411 (2009)","journal-title":"SIAM J. Matrix Anal. A."},{"unstructured":"Yang, K., Pouransari, H., Darve, E.: Sparse hierarchical solvers with guaranteed convergence. arXiv:1611.03189 (2016)","key":"9794_CR30"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09794-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-020-09794-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-020-09794-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,27]],"date-time":"2022-10-27T01:45:46Z","timestamp":1666835146000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-020-09794-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,8]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["9794"],"URL":"https:\/\/doi.org\/10.1007\/s10444-020-09794-y","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2020,6,8]]},"assertion":[{"value":"30 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 May 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 June 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"52"}}