{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T16:44:43Z","timestamp":1787503483585,"version":"build-2736575974"},"reference-count":31,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1318377"],"award-info":[{"award-number":["DMS-1318377"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1613861"],"award-info":[{"award-number":["DMS-1613861"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this paper we propose a new iterative method to hierarchically compute a relatively large number of leftmost eigenpairs of a sparse symmetric positive matrix under the multiresolution operator compression framework. We exploit the well-conditioned property of every decomposition component by integrating the multiresolution framework into the implicitly restarted Lanczos method. We achieve this combination by proposing an extension-refinement iterative scheme, in which the intrinsic idea is to decompose the target spectrum into several segments such that the corresponding eigenproblem in each segment is well-conditioned. Theoretical analysis and numerical illustration are also reported to illustrate the efficiency and effectiveness of this algorithm.<\/jats:p>","DOI":"10.1137\/18m1180827","type":"journal-article","created":{"date-parts":[[2019,1,30]],"date-time":"2019-01-30T13:52:07Z","timestamp":1548856327000},"page":"260-306","source":"Crossref","is-referenced-by-count":6,"title":["A Fast Hierarchically Preconditioned Eigensolver Based on Multiresolution Matrix Decomposition"],"prefix":"10.1137","volume":"17","author":[{"given":"Thomas Y.","family":"Hou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"De","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ka Chun","family":"Lam","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziyun","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,1,30]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s40324-017-0108-2"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1506(199703\/04)4:2<69::AID-NLA98>3.0.CO;2-F"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"E. Bozzo and M. Franceschet,\n                      Effective and Efficient Approximations of the Generalized Inverse of the Graph Laplacian Matrix with an Application to Current-Flow Betweenness Centrality\n                      , preprint, arXiv:1205.4894, 2012.","DOI":"10.1080\/15427951.2012.715115"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.socnet.2013.05.003"},{"key":"atypb5","first-page":"1","volume":"2","author":"Calvetti D.","year":"1994","journal-title":"Electron. Trans. Numer. Anal."},{"key":"atypb6","unstructured":"F. R. Chung,\n                      Spectral Graph Theory\n                      , CBMS Reg. Conf. Ser. 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Owhadi and C. Scovel,\n                      Universal Scalable Robust Solvers from Computational Information Games and Fast Eigenspace Adapted Multiresolution Analysis\n                      , preprint, arXiv:1703.10761, 2017."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1318679110"},{"key":"atypb23","first-page":"380","author":"Romero E.","year":"2010","journal-title":"Berlin"},{"key":"atypb24","unstructured":"F. Sch\u00e4fer, T. Sullivan, and H. Owhadi,\n                      Compression, Inversion, and Approximate PCA of Dense Kernel Matrices at Near-Linear Computational Complexity\n                      , preprint, arXiv:1706.02205, 2017."},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1109\/34.868688"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144599363084"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/0613025"},{"key":"atypb28","first-page":"119","author":"Sorensen D. 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