{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:11:22Z","timestamp":1776784282510,"version":"3.51.2"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"251","license":[{"start":{"date-parts":[[2005,9,17]],"date-time":"2005-09-17T00:00:00Z","timestamp":1126915200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L Superscript normal infinity\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mi mathvariant=\"normal\">\n                              \u221e\n                              \n                            <\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^\\infty<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"script upper H\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">H<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathcal {H}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear complexity.\n                  <\/p>","DOI":"10.1090\/s0025-5718-04-01716-8","type":"journal-article","created":{"date-parts":[[2005,4,12]],"date-time":"2005-04-12T12:20:25Z","timestamp":1113308425000},"page":"1179-1199","source":"Crossref","is-referenced-by-count":54,"title":["Efficient inversion of the Galerkin matrix of general second-order elliptic operators with nonsmooth coefficients"],"prefix":"10.1090","volume":"74","author":[{"given":"Mario","family":"Bebendorf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2004,9,17]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/PL00005410","article-title":"Approximation of boundary element matrices","volume":"86","author":"Bebendorf, Mario","year":"2000","journal-title":"Numer. 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Matrix compression and fast solution","volume":"1","author":"Dahmen, W.","year":"1993","journal-title":"Adv. Comput. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1019-7168","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1007\/BF02571732","article-title":"Wavelet approximation methods for pseudodifferential equations. I. Stability and convergence","volume":"215","author":"Dahmen, W.","year":"1994","journal-title":"Math. 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