{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T11:03:16Z","timestamp":1746183796675,"version":"3.30.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,3,2]],"date-time":"2024-03-02T00:00:00Z","timestamp":1709337600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,3,2]],"date-time":"2024-03-02T00:00:00Z","timestamp":1709337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Women Leading IITM (India) 2022 in Mathematics","award":["SB22230053MAIITM008880"],"award-info":[{"award-number":["SB22230053MAIITM008880"]}]},{"name":"Board of Research in Nuclear Sciences, Department of Atomic Energy, India","award":["34\/20\/03\/2017-BRNS\/34278"],"award-info":[{"award-number":["34\/20\/03\/2017-BRNS\/34278"]}]},{"name":"MATRICS grant from the Science and Engineering Research Board, India","award":["MTR\/2019\/001241"],"award-info":[{"award-number":["MTR\/2019\/001241"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1007\/s11075-024-01765-4","type":"journal-article","created":{"date-parts":[[2024,3,2]],"date-time":"2024-03-02T08:02:26Z","timestamp":1709366546000},"page":"1635-1672","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["HODLR3D: hierarchical matrices for N-body problems in three dimensions"],"prefix":"10.1007","volume":"97","author":[{"given":"Kandappan V.","family":"A","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vaishnavi","family":"Gujjula","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sivaram","family":"Ambikasaran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,2]]},"reference":[{"key":"1765_CR1","unstructured":"Gray, A., Moore, A.: N-body\u2019 problems in statistical learning. Advances in neural information processing systems 13 (2000)"},{"key":"1765_CR2","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.csda.2019.02.002","volume":"137","author":"A Litvinenko","year":"2019","unstructured":"Litvinenko, A., Sun, Y., Genton, M.G., Keyes, D.E.: Likelihood approximation with hierarchical matrices for large spatial datasets. Computational Statistics & Data Analysis. 137, 115\u2013132 (2019)","journal-title":"Computational Statistics & Data Analysis."},{"key":"1765_CR3","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.cma.2016.05.029","volume":"308","author":"P Coulier","year":"2016","unstructured":"Coulier, P., Darve, E.: Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method. Comput. Methods Appl. Mech. Eng. 308, 286\u2013309 (2016)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"5","key":"1765_CR4","doi-asserted-by":"publisher","first-page":"1876","DOI":"10.1137\/060662083","volume":"29","author":"NA Gumerov","year":"2007","unstructured":"Gumerov, N.A., Duraiswami, R.: Fast radial basis function interpolation via preconditioned Krylov iteration. SIAM J. Sci. Comput. 29(5), 1876\u20131899 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"1765_CR5","doi-asserted-by":"crossref","unstructured":"Hackbusch, W.: A sparse matrix arithmetic based on H-matrices. part i:Introduction to H-matrices. Computing. 62(2), 89\u2013108 (1999)","DOI":"10.1007\/s006070050015"},{"issue":"4","key":"1765_CR6","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s00607-003-0019-1","volume":"70","author":"L Grasedyck","year":"2003","unstructured":"Grasedyck, L., Hackbusch, W.: Construction and arithmetics of H-matrices. Computing 70(4), 295\u2013334 (2003)","journal-title":"Computing"},{"issue":"5","key":"1765_CR7","doi-asserted-by":"publisher","first-page":"2382","DOI":"10.1137\/22M1491253","volume":"45","author":"VA Kandappan","year":"2023","unstructured":"Kandappan, V.A., Gujjula, V., Ambikasaran, S.: HODLR2D: a new class of hierarchical matrices. SIAM J. Sci. Comput. 45(5), 2382\u20132408 (2023). https:\/\/doi.org\/10.1137\/22M1491253","journal-title":"SIAM J. Sci. Comput."},{"key":"1765_CR8","doi-asserted-by":"crossref","unstructured":"Barnes, J., Hut, P.: A hierarchical O (N log N) force-calculation algorithm. Nature. 324(6096), 446\u2013449 (1986)","DOI":"10.1038\/324446a0"},{"issue":"2","key":"1765_CR9","doi-asserted-by":"publisher","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."},{"key":"1765_CR10","doi-asserted-by":"crossref","unstructured":"Greengard, L.: The rapid evaluation of potential fields in particle systems. MIT Press, (1988)","DOI":"10.7551\/mitpress\/5750.001.0001"},{"key":"1765_CR11","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1017\/S0962492900002725","volume":"6","author":"L Greengard","year":"1997","unstructured":"Greengard, L., Rokhlin, V.: A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numer 6, 229\u2013269 (1997)","journal-title":"Acta Numer"},{"key":"1765_CR12","unstructured":"Ambikasaran, S.: Fast algorithms for dense numerical linear algebra and applications. PhD thesis, Stanford University (2013)"},{"issue":"3","key":"1765_CR13","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s10915-013-9714-z","volume":"57","author":"S Ambikasaran","year":"2013","unstructured":"Ambikasaran, S., Darve, E.: An $$\\cal{O} (n \\log n)$$-fast direct solver for partial hierarchically semi-separable matrices. J. Sci. Comput. 57(3), 477\u2013501 (2013). https:\/\/doi.org\/10.1007\/s10915-013-9714-z","journal-title":"J. Sci. Comput."},{"issue":"2","key":"1765_CR14","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1137\/S0895479802405884","volume":"27","author":"S Chandrasekaran","year":"2005","unstructured":"Chandrasekaran, S., Dewilde, P., Gu, M., Pals, T., Sun, X., Veen, A.-J., White, D.: Some fast algorithms for sequentially semiseparable representations. SIAM J. Matrix Anal. Appl. 27(2), 341\u2013364 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"3","key":"1765_CR15","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10092-005-0107-z","volume":"42","author":"R Vandebril","year":"2005","unstructured":"Vandebril, R., Barel, M.V., Golub, G., Mastronardi, N.: A bibliography on semiseparable matrices. Calcolo 42(3), 249\u2013270 (2005)","journal-title":"Calcolo"},{"issue":"8","key":"1765_CR16","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1002\/nla.455","volume":"12","author":"R Vandebril","year":"2005","unstructured":"Vandebril, R., Van Barel, M., Mastronardi, N.: A note on the representation and definition of semiseparable matrices. Numerical Linear Algebra with Applications. 12(8), 839\u2013858 (2005)","journal-title":"Numerical Linear Algebra with Applications."},{"key":"1765_CR17","first-page":"2003","volume":"21","author":"S B\u00f6rm","year":"2003","unstructured":"B\u00f6rm, S., Grasedyck, L., Hackbusch, W.: Hierarchical matrices. Lecture notes. 21, 2003 (2003)","journal-title":"Hierarchical matrices. Lecture notes."},{"issue":"5","key":"1765_CR18","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. Boundary Elem. 27(5), 405\u2013422 (2003)","journal-title":"Eng. Anal. Boundary Elem."},{"key":"1765_CR19","doi-asserted-by":"crossref","unstructured":"Hackbusch, W.: Hierarchical matrices: algorithms and analysis vol. 49. Springer (2015)","DOI":"10.1007\/978-3-662-47324-5"},{"key":"1765_CR20","doi-asserted-by":"crossref","unstructured":"Yokota, R., Ibeid, H., Keyes, D.: Fast multipole method as a matrix-free hierarchical low-rank approximation. In: International Workshop on Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, pp. 267\u2013286 (2015). Springer","DOI":"10.1007\/978-3-319-62426-6_17"},{"key":"1765_CR21","doi-asserted-by":"crossref","unstructured":"Amestoy, P., Ashcraft, C., Boiteau, O., Buttari, A., l\u2019Excellent, J.-Y., Weisbecker, C.: Improving multifrontal methods by means of block low-rank representations. SIAM Journal on Scientific Computing. 37(3), 1451\u20131474 (2015)","DOI":"10.1137\/120903476"},{"key":"1765_CR22","doi-asserted-by":"crossref","unstructured":"Amestoy, P., Buttari, A., l\u2019Excellent, J.-Y., Mary, T.: On the complexity of the block low-rank multifrontal factorization. SIAM Journal on Scientific Computing. 39(4), 1710\u20131740 (2017)","DOI":"10.1137\/16M1077192"},{"key":"1765_CR23","unstructured":"Khan, R., Kandappan, V., Ambikasaran, S.: Numerical rank of singular kernel functions. arXiv:2209.05819 (2022)"},{"issue":"3","key":"1765_CR24","doi-asserted-by":"publisher","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"},{"key":"1765_CR25","first-page":"1","volume":"1","author":"R Beatson","year":"1997","unstructured":"Beatson, R., Greengard, L.: A short course on fast multipole methods. Wavelets, multilevel methods and elliptic PDEs. 1, 1\u201337 (1997)","journal-title":"Wavelets, multilevel methods and elliptic PDEs."},{"issue":"1","key":"1765_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00607-002-1469-6","volume":"70","author":"M Bebendorf","year":"2003","unstructured":"Bebendorf, M., Rjasanow, S.: Adaptive low-rank approximation of collocation matrices. Computing 70(1), 1\u201324 (2003)","journal-title":"Computing"},{"issue":"4","key":"1765_CR27","doi-asserted-by":"publisher","first-page":"763","DOI":"10.1109\/TEMC.2005.857898","volume":"47","author":"K Zhao","year":"2005","unstructured":"Zhao, K., Vouvakis, M.N., Lee, J.-F.: The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems. IEEE Trans. Electromagn. Compat. 47(4), 763\u2013773 (2005)","journal-title":"IEEE Trans. Electromagn. Compat."},{"issue":"4","key":"1765_CR28","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/s006070070031","volume":"64","author":"E Tyrtyshnikov","year":"2000","unstructured":"Tyrtyshnikov, E.: Incomplete cross approximation in the mosaic-skeleton method. Computing 64(4), 367\u2013380 (2000)","journal-title":"Computing"},{"issue":"4","key":"1765_CR29","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/PL00005410","volume":"86","author":"M Bebendorf","year":"2000","unstructured":"Bebendorf, M.: Approximation of boundary element matrices. Numer. Math. 86(4), 565\u2013589 (2000)","journal-title":"Numer. Math."},{"key":"1765_CR30","doi-asserted-by":"crossref","unstructured":"Bebendorf, M., Kunis, S.: Recompression techniques for adaptive cross approximation. The Journal of Integral Equations and Applications, 331\u2013357 (2009)","DOI":"10.1216\/JIE-2009-21-3-331"},{"key":"1765_CR31","doi-asserted-by":"crossref","unstructured":"Barrett, R., Berry, M., Chan, T.F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., Vorst, H.: Templates for the solution of linear systems: building blocks for iterative methods. SIAM, (1994)","DOI":"10.1137\/1.9781611971538"},{"issue":"3","key":"1765_CR32","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856\u2013869 (1986)","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"1765_CR33","unstructured":"Izadi, M.: Hierarchical matrix techniques on massively parallel computers. Thesis (2012)"},{"key":"1765_CR34","unstructured":"Li, Y., Poulson, J., Ying, L.: Distributed-memory $$\\cal{H}$$-matrix algebra I: data distribution and matrix-vector multiplication. arXiv:2008.12441 (2020)"},{"key":"1765_CR35","unstructured":"Ambikasaran, S., Darve, E.: The inverse fast multipole method. arXiv:1407.1572 (2014)"},{"key":"1765_CR36","doi-asserted-by":"crossref","unstructured":"Gujjula, V., Ambikasaran, S.: Algebraic inverse fast multipole method: a fast direct solver that is better than HODLR based fast direct solver. arXiv:2301.12704 (2023)","DOI":"10.1016\/j.jcp.2023.112627"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01765-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01765-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01765-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T09:24:24Z","timestamp":1732785864000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01765-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,2]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["1765"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01765-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2024,3,2]]},"assertion":[{"value":"28 September 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"The authors declare no competing interests.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}