{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T17:17:37Z","timestamp":1773249457720,"version":"3.50.1"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"5-6","license":[{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,11,13]],"date-time":"2019-11-13T00:00:00Z","timestamp":1573603200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["F65"],"award-info":[{"award-number":["F65"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002848","name":"Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica","doi-asserted-by":"crossref","award":["FONDECYT 1170672"],"award-info":[{"award-number":["FONDECYT 1170672"]}],"id":[{"id":"10.13039\/501100002848","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":[[2019,12]]},"DOI":"10.1007\/s10444-019-09718-5","type":"journal-article","created":{"date-parts":[[2019,11,12]],"date-time":"2019-11-12T21:02:48Z","timestamp":1573592568000},"page":"2893-2919","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["${\\mathscr{H}}$-matrix approximability of inverses of discretizations of the fractional Laplacian"],"prefix":"10.1007","volume":"45","author":[{"given":"Michael","family":"Karkulik","sequence":"first","affiliation":[]},{"given":"Jens Markus","family":"Melenk","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,11,13]]},"reference":[{"issue":"4","key":"9718_CR1","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1016\/j.camwa.2017.05.026","volume":"74","author":"G Acosta","year":"2017","unstructured":"Acosta, G., Bersetche, F.M., Borthagaray, J.P.: A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. Comput. Math Appl. 74(4), 784\u2013816 (2017)","journal-title":"Comput. Math Appl."},{"issue":"2","key":"9718_CR2","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1137\/15M1033952","volume":"55","author":"G Acosta","year":"2017","unstructured":"Acosta, G., Borthagaray, J.P.: A fractional Laplace equation: regularity of solutions and finite element approximations. SIAM J. Numer. Anal. 55(2), 472\u2013495 (2017)","journal-title":"SIAM J. Numer. Anal."},{"key":"9718_CR3","volume-title":"Sobolev Spaces, Volume 140 of Pure and Applied Mathematics (Amsterdam)","author":"RA Adams","year":"2003","unstructured":"Adams, R.A., Fournier, J.J.F.: Sobolev Spaces, Volume 140 of Pure and Applied Mathematics (Amsterdam), 2nd edn. Elsevier\/Academic Press, Amsterdam (2003)","edition":"2nd edn."},{"key":"9718_CR4","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.cma.2017.08.019","volume":"327","author":"M Ainsworth","year":"2017","unstructured":"Ainsworth, M., Glusa, C.: Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver. Comput. Methods Appl. Mech. Engrg. 327, 4\u201335 (2017)","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"issue":"4","key":"9718_CR5","doi-asserted-by":"crossref","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."},{"issue":"3","key":"9718_CR6","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"},{"issue":"4","key":"9718_CR7","doi-asserted-by":"crossref","first-page":"1472","DOI":"10.1137\/060669747","volume":"45","author":"M Bebendorf","year":"2007","unstructured":"Bebendorf, M.: Why finite element discretizations can be factored by triangular hierarchical matrices. SIAM J. Numer. Anal. 45(4), 1472\u20131494 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"9718_CR8","doi-asserted-by":"crossref","unstructured":"Bonito, A., Lei, W., Pasciak, J.E.: On sinc quadrature approximations of fractional powers of regularly accretive operators. ArXiv e-prints (2017)","DOI":"10.1093\/imanum\/drw042"},{"issue":"295","key":"9718_CR9","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1090\/S0025-5718-2015-02937-8","volume":"84","author":"A Bonito","year":"2015","unstructured":"Bonito, A., Pasciak, J. : Numerical approximation of fractional powers of elliptic operators. Math. Comp. 84(295), 2083\u20132110 (2015)","journal-title":"Math. Comp."},{"issue":"2","key":"9718_CR10","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s00211-009-0278-7","volume":"115","author":"S B\u00f6rm","year":"2010","unstructured":"B\u00f6rm, S.: Approximation of solution operators of elliptic partial differential equations by ${\\mathscr{H}}^{2}$-matrices. Numer. Math. 115(2), 165\u2013193 (2010)","journal-title":"Numer. Math."},{"key":"9718_CR11","doi-asserted-by":"crossref","DOI":"10.4171\/091","volume-title":"Efficient Numerical Methods for Non-Local Operators, Volume 14 of EMS Tracts in Mathematics","author":"S B\u00f6rm","year":"2010","unstructured":"B\u00f6rm, S.: Efficient Numerical Methods for Non-Local Operators, Volume 14 of EMS Tracts in Mathematics. European Mathematical Society (EMS), Z\u00fcrich (2010)"},{"issue":"2","key":"9718_CR12","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/s00211-005-0618-1","volume":"101","author":"S B\u00f6rm","year":"2005","unstructured":"B\u00f6rm, S., Grasedyck, L.: Hybrid cross approximation of integral operators. Numer. Math. 101(2), 221\u2013249 (2005)","journal-title":"Numer. Math."},{"issue":"1","key":"9718_CR13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.anihpc.2013.02.001","volume":"31","author":"X Cabr\u00e9","year":"2014","unstructured":"Cabr\u00e9, X., Sire, Y.: Nonlinear equations for fractional Laplacians, I Regularity, maximum principles, and Hamiltonian estimates. Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire 31(1), 23\u201353 (2014)","journal-title":"Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"issue":"5","key":"9718_CR14","doi-asserted-by":"crossref","first-page":"2052","DOI":"10.1016\/j.aim.2010.01.025","volume":"224","author":"X Cabr\u00e9","year":"2010","unstructured":"Cabr\u00e9, X., Tan, J.: Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224(5), 2052\u20132093 (2010)","journal-title":"Adv. Math."},{"issue":"7-9","key":"9718_CR15","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1080\/03605300600987306","volume":"32","author":"L Caffarelli","year":"2007","unstructured":"Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Comm. Partial Diff. Equ. 32(7-9), 1245\u20131260 (2007)","journal-title":"Comm. Partial Diff. Equ."},{"issue":"3","key":"9718_CR16","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1016\/j.anihpc.2015.01.004","volume":"33","author":"L Caffarelli","year":"2016","unstructured":"Caffarelli, L., Stinga, P.: Fractional elliptic equations, Caccioppoli estimates and regularity. Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire 33(3), 767\u2013807 (2016)","journal-title":"Ann. Inst. H. Poincar\u00e9, Anal. Non Lin\u00e9aire"},{"issue":"8","key":"9718_CR17","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1080\/03605302.2011.562954","volume":"36","author":"A Capella","year":"2011","unstructured":"Capella, A., D\u00e1vila, J., Dupaigne, L., Sire, Y.: Regularity of radial extremal solutions for some non-local semilinear equations. Comm Partial Diff. Equ. 36(8), 1353\u20131384 (2011)","journal-title":"Comm Partial Diff. Equ."},{"issue":"2","key":"9718_CR18","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1016\/j.acha.2014.04.002","volume":"38","author":"E Corona","year":"2015","unstructured":"Corona, E., Martinsson, P.-G., Zorin, D.: An O(N) direct solver for integral equations on the plane. Appl. Comput. Harmon. Anal. 38(2), 284\u2013317 (2015)","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"9718_CR19","doi-asserted-by":"crossref","first-page":"305","DOI":"10.5802\/aif.55","volume":"5","author":"J Deny","year":"1955","unstructured":"Deny, J., Lions, J.L.: Les espaces du type de Beppo Levi. Ann. Fourier, Grenoble 5, 305\u2013370 (1955). 1953\u201354","journal-title":"Ann. Fourier, Grenoble"},{"issue":"4","key":"9718_CR20","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.1007\/s00211-016-0825-y","volume":"135","author":"J D\u00f6lz","year":"2017","unstructured":"D\u00f6lz, J., Harbrecht, H., Schwab, C.: Covariance regularity and ${\\mathscr{H}}$-matrix approximation for rough random fields. Numer. Math. 135(4), 1045\u20131071 (2017)","journal-title":"Numer. Math."},{"key":"9718_CR21","unstructured":"Duan, R., Lazarov, R., P.J.: Numerical approximation of fractional powers of elliptic operators. Technical report, arXiv:1803.10055 (2018)"},{"issue":"4","key":"9718_CR22","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1007\/s00211-015-0706-9","volume":"131","author":"M Faustmann","year":"2015","unstructured":"Faustmann, M., Melenk, J.M., Praetorius, D.: ${\\mathscr{H}}$-matrix approximability of the inverses of FEM matrices. Numer. Math. 131(4), 615\u2013642 (2015)","journal-title":"Numer. Math."},{"issue":"297","key":"9718_CR23","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1090\/mcom\/2990","volume":"85","author":"M Faustmann","year":"2016","unstructured":"Faustmann, M., Melenk, J.M., Praetorius, D.: Existence of ${\\mathscr{H}}$-matrix approximants to the inverses of BEM matrices: the simple-layer operator. Math. Comp. 85(297), 119\u2013152 (2016)","journal-title":"Math. Comp."},{"issue":"3","key":"9718_CR24","first-page":"1211","volume":"37","author":"M Faustmann","year":"2017","unstructured":"Faustmann, M., Melenk, J.M., Praetorius, D.: Existence of ${\\mathscr{H}}$-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator. IMA J. Numer. Anal. 37(3), 1211\u20131244 (2017)","journal-title":"IMA J. Numer. Anal."},{"key":"9718_CR25","first-page":"284","volume":"27","author":"E Gagliardo","year":"1957","unstructured":"Gagliardo, E.: Caratterizzazioni delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Sem. Mat. Univ. Padova 27, 284\u2013305 (1957)","journal-title":"Rend. Sem. Mat. Univ. Padova"},{"issue":"2","key":"9718_CR26","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s00607-004-0086-y","volume":"74","author":"IP Gavrilyuk","year":"2005","unstructured":"Gavrilyuk, I.P., Hackbusch, W., Khoromskij, B.N.: Hierarchical tensor-product approximation to the inverse and related operators for high-dimensional elliptic problems. Computing 74(2), 131\u2013157 (2005)","journal-title":"Computing"},{"issue":"4","key":"9718_CR27","doi-asserted-by":"crossref","first-page":"A2023","DOI":"10.1137\/130918988","volume":"36","author":"A Gillman","year":"2014","unstructured":"Gillman, A., Martinsson, P.G.: A direct solver with O(N) complexity for variable coefficient elliptic PDEs discretized via a high-order composite spectral collocation method. SIAM J. Sci. Comput. 36(4), A2023\u2013A2046 (2014)","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"9718_CR28","doi-asserted-by":"crossref","first-page":"3829","DOI":"10.1090\/S0002-9947-09-04615-7","volume":"361","author":"V Gol\u2019dshtein","year":"2009","unstructured":"Gol\u2019dshtein, V., Ukhlov, A.: Weighted Sobolev spaces and embedding theorems. Trans. Amer. Math. Soc. 361(7), 3829\u20133850 (2009)","journal-title":"Trans. Amer. Math. Soc."},{"key":"9718_CR29","unstructured":"Grasedyck, L.: Theorie und Anwendungen Hierarchischer Matrizen. Doctoral thesis Kiel (2001)"},{"issue":"3","key":"9718_CR30","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s00607-004-0103-1","volume":"74","author":"L Grasedyck","year":"2005","unstructured":"Grasedyck, L.: Adaptive recompression of ${\\mathscr{H}}$-matrices for BEM. Computing 74(3), 205\u2013223 (2005)","journal-title":"Computing"},{"issue":"4","key":"9718_CR31","doi-asserted-by":"crossref","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 ${\\mathscr{H}}$-matrices. Computing 70(4), 295\u2013334 (2003)","journal-title":"Computing"},{"issue":"4","key":"9718_CR32","doi-asserted-by":"crossref","first-page":"336","DOI":"10.2478\/cmam-2008-0024","volume":"8","author":"L Grasedyck","year":"2008","unstructured":"Grasedyck, L., Hackbusch, W., Kriemann, R.: Performance of ${\\mathscr{H}}$-LU preconditioning for sparse matrices. Comput. Methods Appl. Math. 8(4), 336\u2013349 (2008)","journal-title":"Comput. Methods Appl. Math."},{"issue":"4-6","key":"9718_CR33","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s00791-008-0098-9","volume":"11","author":"L Grasedyck","year":"2008","unstructured":"Grasedyck, L., Kriemann, R., Le Borne, S.: Parallel black box ${\\mathscr{H}}$-LU preconditioning for elliptic boundary value problems. Comput. Vis. Sci. 11(4-6), 273\u2013291 (2008)","journal-title":"Comput. Vis. Sci."},{"key":"9718_CR34","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1017\/S0962492906410011","volume":"18","author":"L Greengard","year":"2009","unstructured":"Greengard, L., Gueyffier, D., Martinsson, P., Rokhlin, V.: Fast direct solvers for integral equations in complex three-dimensional domains. Acta Numer. 18, 243\u2013275 (2009)","journal-title":"Acta Numer."},{"issue":"2","key":"9718_CR35","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. Introduction to ${\\mathscr{H}}$-matrices. Computing 62(2), 89\u2013108 (1999)","journal-title":"Computing"},{"key":"9718_CR36","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-47324-5","volume-title":"Hierarchical Matrices: Algorithms and Analysis, Volume 49 of Springer Series in Computational Mathematics","author":"W Hackbusch","year":"2015","unstructured":"Hackbusch, W.: Hierarchical Matrices: Algorithms and Analysis, Volume 49 of Springer Series in Computational Mathematics. Springer, Heidelberg (2015)"},{"key":"9718_CR37","doi-asserted-by":"crossref","unstructured":"Hackbusch, W., Khoromskij, B., Sauter, S.: On ${\\mathscr{H}}^{2}$-matrices. Lect. Appl. Math., 9\u201329 (2000)","DOI":"10.1007\/978-3-642-59709-1_2"},{"issue":"1-2","key":"9718_CR38","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/S0377-0427(00)00486-6","volume":"125","author":"W Hackbusch","year":"2000","unstructured":"Hackbusch, W., Khoromskij, B.N.: A sparse ${\\mathscr{H}}$-matrix arithmetic: general complexity estimates. J. Comput. Appl. Math. 125(1-2), 479\u2013501 (2000)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"9718_CR39","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 ${\\mathscr{H}}$-matrix arithmetic. II. Application to multi-dimensional problems. Computing 64(1), 21\u201347 (2000)","journal-title":"Computing"},{"issue":"5","key":"9718_CR40","doi-asserted-by":"crossref","first-page":"2505","DOI":"10.1137\/070700607","volume":"46","author":"N Hale","year":"2008","unstructured":"Hale, N., Higham, N.J., Trefethen, L.N.: Computing A $^{{\\alpha }},\\log (A)$, and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46(5), 2505\u20132523 (2008)","journal-title":"SIAM J. Numer. Anal."},{"issue":"5","key":"9718_CR41","doi-asserted-by":"crossref","first-page":"e2167,24","DOI":"10.1002\/nla.2167","volume":"25","author":"S Harizanov","year":"2018","unstructured":"Harizanov, S., Lazarov, R., Margenov, S., Marinov, P., Vutov, Y.: Optimal solvers for linear systems with fractional powers of sparse SPD matrices. Numer Linear Algebra Appl. 25(5), e2167,24 (2018)","journal-title":"Numer Linear Algebra Appl."},{"key":"9718_CR42","unstructured":"Heidel, G., Khoromskaia, V., Khoromskij, B., Schulz, V.: Tensor approach to optimal control problems with fractional d-dimensional elliptic operator in constraints. Technical report, arXiv:1809.01971 (2018)"},{"issue":"5","key":"9718_CR43","doi-asserted-by":"crossref","first-page":"A2507","DOI":"10.1137\/120866683","volume":"34","author":"K Ho","year":"2012","unstructured":"Ho, K., Greengard, L.: A fast direct solver for structured linear systems by recursive skeletonization. SIAM J. Sci Comput. 34(5), A2507\u2013A2532 (2012)","journal-title":"SIAM J. Sci Comput."},{"issue":"8","key":"9718_CR44","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1002\/cpa.21582","volume":"69","author":"KL Ho","year":"2016","unstructured":"Ho, K.L., Ying, L.: Hierarchical interpolative factorization for elliptic operators: differential equations. Comm. Pure Appl. Math. 69(8), 1415\u20131451 (2016)","journal-title":"Comm. Pure Appl. Math."},{"issue":"7","key":"9718_CR45","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1002\/cpa.21577","volume":"69","author":"KL Ho","year":"2016","unstructured":"Ho, K.L., Ying, L.: Hierarchical interpolative factorization for elliptic operators: integral equations. Comm. Pure Appl. Math. 69(7), 1314\u20131353 (2016)","journal-title":"Comm. Pure Appl. Math."},{"key":"9718_CR46","volume-title":"Weighted Sobolev Spaces. A Wiley-Interscience Publication","author":"A Kufner","year":"1985","unstructured":"Kufner, A.: Weighted Sobolev Spaces. A Wiley-Interscience Publication. Wiley, New York (1985). Translated from the Czech"},{"issue":"1","key":"9718_CR47","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1515\/fca-2017-0002","volume":"20","author":"M Kwa\u015bnicki","year":"2017","unstructured":"Kwa\u015bnicki, M.: Ten equivalent definitions of the fractional Laplace operator. Fract. Calc. Appl. Anal. 20(1), 7\u201351 (2017)","journal-title":"Fract. Calc. Appl. Anal."},{"issue":"4","key":"9718_CR48","doi-asserted-by":"crossref","first-page":"1172","DOI":"10.1137\/040615845","volume":"27","author":"S Le Borne","year":"2006","unstructured":"Le Borne, S., Grasedyck, L.: ${\\mathscr{H}}$-matrix preconditioners in convection-dominated problems. SIAM J. Matrix Anal. Appl. 27 (4), 1172\u20131183 (2006). (electronic)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9718_CR49","unstructured":"Li, I., Mao, Z., Song, F., Wang, H., Karniadakis, G.: A fast solver for spectral element approximation applied to fractional differential equations using hierarchical matrix approximation. Technical report https:\/\/arxiv.org\/pdf\/1808.02937.pdf (2018)"},{"issue":"3","key":"9718_CR50","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1137\/110851110","volume":"33","author":"S Li","year":"2012","unstructured":"Li, S., Gu, M., Wu, C., Xia, J.: New efficient and robust HSS Cholesky factorization of SPD matrices. SIAM J. Matrix Anal. Appl. 33(3), 886\u2013904 (2012)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9718_CR51","unstructured":"Lischke, A., Pang, G., Gulian, M., Song, F., Glusa, C., Zheng, X., Mao, Z., Cai, W., Meers chaert, M., Ainsworth, M., Karniadakis, G.: What is the fractional Laplacian? Technical report, arxiv:1801.09767, 01 (2018)"},{"issue":"3","key":"9718_CR52","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1007\/s10915-008-9240-6","volume":"38","author":"P Martinsson","year":"2009","unstructured":"Martinsson, P.: A fast direct solver for a class of elliptic partial differential equations. J. Sci. Comput. 38(3), 316\u2013330 (2009)","journal-title":"J. Sci. Comput."},{"issue":"1","key":"9718_CR53","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jcp.2004.10.033","volume":"205","author":"P Martinsson","year":"2005","unstructured":"Martinsson, P., 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."},{"key":"9718_CR54","doi-asserted-by":"crossref","first-page":"31","DOI":"10.4064\/sm-44-1-31-38","volume":"44","author":"B Muckenhoupt","year":"1972","unstructured":"Muckenhoupt, B.: Hardy\u2019s inequality with weights. Studia Math. 44, 31\u201338 (1972). Collection of articles honoring the completion by Antoni Zygmund of 50 years of scientific activity, I","journal-title":"Studia Math."},{"issue":"1","key":"9718_CR55","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/s00211-015-0709-6","volume":"132","author":"RH Nochetto","year":"2016","unstructured":"Nochetto, R.H., Ot\u00e1rola, E., Salgado, A.J.: Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications. Numer. Math. 132(1), 85\u2013130 (2016)","journal-title":"Numer. Math."},{"issue":"4","key":"9718_CR56","doi-asserted-by":"crossref","first-page":"1314","DOI":"10.1016\/j.jcp.2011.10.013","volume":"231","author":"P Schmitz","year":"2012","unstructured":"Schmitz, P., Ying, L.: A fast direct solver for elliptic problems on general meshes in 2D. J. Comput. Phys. 231(4), 1314\u20131338 (2012)","journal-title":"J. Comput. Phys."},{"issue":"190","key":"9718_CR57","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1090\/S0025-5718-1990-1011446-7","volume":"54","author":"LR Scott","year":"1990","unstructured":"Scott, L.R., Zhang, S.: Finite element interpolation of nonsmooth functions satisfying boundary conditions. Math. Comp. 54(190), 483\u2013493 (1990)","journal-title":"Math. Comp."},{"issue":"11","key":"9718_CR58","doi-asserted-by":"crossref","first-page":"2092","DOI":"10.1080\/03605301003735680","volume":"35","author":"P Stinga","year":"2010","unstructured":"Stinga, P., Torrea, J.: Extension problem and Harnack\u2019s inequality for some fractional operators. Comm. Partial Diff. Equ. 35(11), 2092\u20132122 (2010)","journal-title":"Comm. Partial Diff. Equ."},{"issue":"2","key":"9718_CR59","doi-asserted-by":"crossref","first-page":"A832","DOI":"10.1137\/120867032","volume":"35","author":"J Xia","year":"2013","unstructured":"Xia, J.: Efficient structured multifrontal factorization for general large sparse matrices. SIAM J. Sci. Comput. 35(2), A832\u2013A860 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"9718_CR60","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.: Superfast multifrontal method for large structured linear systems of equations. SIAM J Matrix Anal. Appl. 31(3), 1382\u20131411 (2009)","journal-title":"SIAM J Matrix Anal. Appl."},{"key":"9718_CR61","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.cma.2017.06.017","volume":"325","author":"X Zhao","year":"2017","unstructured":"Zhao, X., Hu, X., Cai, W., Karniadakis, G.E : Adaptive finite element method for fractional differential equations using hierarchical matrices. Comput. Methods Appl. Mech Engrg. 325, 56\u201376 (2017)","journal-title":"Comput. Methods Appl. Mech Engrg."},{"key":"9718_CR62","unstructured":"Zygmund, A.: Trigonometric Series. Cambridge Mathematical Library, 3rd edn., vol. I, II. Cambridge University Press, Cambridge (2002). With a foreword by Robert A. Fefferman"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09718-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-019-09718-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-019-09718-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,4]],"date-time":"2022-10-04T10:13:45Z","timestamp":1664878425000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-019-09718-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,13]]},"references-count":62,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["9718"],"URL":"https:\/\/doi.org\/10.1007\/s10444-019-09718-5","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,13]]},"assertion":[{"value":"1 October 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 August 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}