{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T10:53:39Z","timestamp":1717584819510},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"name":"National Science Foundation","award":["CMMI-0969150"],"award-info":[{"award-number":["CMMI-0969150"]}]},{"name":"National Science Foundation","award":["CMMI-1265511"],"award-info":[{"award-number":["CMMI-1265511"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014,6,1]]},"abstract":"<jats:title>Abstract.<\/jats:title>\n               <jats:p>Random matrices, that is, matrices whose entries are measurable\nfunctions of a random vector <jats:italic>Z<\/jats:italic>, are encountered in finite\nelement\/difference formulations of a broad range of stochastic\nmechanics problems. Monte Carlo simulation, the only general\nmethod for solving this class of problems, is usual impractical\nwhen dealing with realistic problems.\nA new method is proposed for solving this class of problems. The\nmethod can be viewed as a smart Monte Carlo simulation. Like Monte\nCarlo, it calculates statistics for quantities of interest from\ndeterministic matrices corresponding to samples of <jats:italic>Z<\/jats:italic>. In\ncontract to Monte Carlo that uses a large number of samples of <jats:italic>Z<\/jats:italic>\nselected at random, the proposed method uses a small number of\nsamples of this vector selected in an optimal manner. The method\nis based on stochastic reduced models (SROMs) for <jats:italic>Z<\/jats:italic>, i.e.,\nrandom vectors with finite numbers of samples, and surrogate\nmodels expressing quantities of interest as known functions of\n<jats:italic>Z<\/jats:italic>.\nTheoretical arguments are followed by numerical examples providing\nstatistics for inverses of random matrices, solutions of\nstochastic algebraic equations, and eigenvalues\/eigenvectors of\nrandom matrices.<\/jats:p>","DOI":"10.1515\/mcma-2013-0021","type":"journal-article","created":{"date-parts":[[2014,5,21]],"date-time":"2014-05-21T12:49:47Z","timestamp":1400676587000},"page":"121-136","source":"Crossref","is-referenced-by-count":4,"title":["An efficient Monte Carlo solution for\nproblems with random matrices"],"prefix":"10.1515","volume":"20","author":[{"given":"Mircea","family":"Grigoriu","sequence":"first","affiliation":[{"name":"Cornell University, Ithaca NY 14853\u20133501, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2014,4,24]]},"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0021\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T21:35:33Z","timestamp":1680384933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2013-0021\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,24]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,4,24]]},"published-print":{"date-parts":[[2014,6,1]]}},"alternative-id":["10.1515\/mcma-2013-0021"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2013-0021","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,4,24]]}}}