{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:05Z","timestamp":1753881245817,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2010,12,9]],"date-time":"2010-12-09T00:00:00Z","timestamp":1291852800000},"content-version":"vor","delay-in-days":342,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Electrical and Computer Engineering"],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>Sparse approximate inverses <jats:italic>M<\/jats:italic> which satisfy min<jats:sub><jats:italic>M<\/jats:italic><\/jats:sub>\u2225<jats:italic>A<\/jats:italic><jats:italic>M<\/jats:italic>\u2212<jats:italic>I<\/jats:italic>\u2225<jats:sub><jats:italic>F<\/jats:italic><\/jats:sub>\n have shown to be an attractive alternative to classical\nsmoothers like Jacobi or Gauss\u2010Seidel (Tang and Wan; 2000). \nThe static and dynamic computation of a SAI and a SPAI\n(Grote and Huckle; 1997), respectively, comes along with advantages like\ninherent parallelism and robustness with equal smoothing\nproperties (Br\u00f6ker et al.; 2001). Here, we are interested in\ndeveloping preconditioners that can incorporate probing conditions\nfor improving the approximation relative to high\u2010 or low\u2010frequency\nsubspaces. We present analytically derived optimal smoothers for\nthe discretization of the constant\u2010coefficient Laplace operator. \nOn this basis, we introduce probing conditions in the\ngeneralized Modified SPAI (MSPAI) approach (Huckle and Kallischko; 2007)\nwhich yields efficient smoothers for multigrid. In the second\npart, we transfer our approach to the domain of ill\u2010posed problems to\nrecover original information from blurred signals. Using the probing\nfacility of MSPAI, we impose the preconditioner to act as\napproximately zero on the noise subspace. In combination with an\niterative regularization method, it thus becomes possible to\nreconstruct the original information more accurately in many cases. \nA variety of numerical results demonstrate the usefulness of this approach.<\/jats:p>","DOI":"10.1155\/2010\/930218","type":"journal-article","created":{"date-parts":[[2010,12,9]],"date-time":"2010-12-09T19:36:20Z","timestamp":1291923380000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Smoothing and Regularization with Modified Sparse Approximate Inverses"],"prefix":"10.1155","volume":"2010","author":[{"given":"T.","family":"Huckle","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Sedlacek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2010,12,9]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1984-0758197-9"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207160701396387"},{"key":"e_1_2_5_3_2","unstructured":"KallischkoA. Modified sparse approximate inverses (MSPAI) for parallel preconditioning Ph.D. thesis 2008 Technische Universit\u00e4t M\u00fcnchen."},{"key":"e_1_2_5_4_2","first-page":"127","article-title":"Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems","volume":"22","author":"Benson M. 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TR-2007-020 Emory University Atlanta Ga USA Proceedings of the Advanced Maui Opticaland Space Surveillance Technologies (AMOS) Conference."},{"key":"e_1_2_5_23_2","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759528507X"},{"key":"e_1_2_5_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02149761"},{"key":"e_1_2_5_25_2","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000027762.08431.64"},{"key":"e_1_2_5_26_2","doi-asserted-by":"publisher","DOI":"10.1137\/1034115"}],"container-title":["Journal of Electrical and Computer Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jece\/2010\/930218.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jece\/2010\/930218.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2010\/930218","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T10:25:43Z","timestamp":1718792743000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2010\/930218"}},"subtitle":[],"editor":[{"given":"Owe","family":"Axelsson","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":26,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1155\/2010\/930218"],"URL":"https:\/\/doi.org\/10.1155\/2010\/930218","archive":["Portico"],"relation":{},"ISSN":["2090-0147","2090-0155"],"issn-type":[{"type":"print","value":"2090-0147"},{"type":"electronic","value":"2090-0155"}],"subject":[],"published":{"date-parts":[[2010,1]]},"assertion":[{"value":"2010-09-20","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-09-22","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-12-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"930218"}}