{"id":285,"date":"2016-08-02T10:03:46","date_gmt":"2016-08-02T01:03:46","guid":{"rendered":"http:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/?p=285"},"modified":"2016-08-02T10:03:46","modified_gmt":"2016-08-02T01:03:46","slug":"%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-85","status":"publish","type":"post","link":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/2016\/08\/02\/%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-85\/","title":{"rendered":"\u300c\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0\u300d\u30bb\u30df\u30ca\u30fc\u6848\u5185 (8\/5)"},"content":{"rendered":"<p>\u65e5\u6642\uff1a\u30002016\u5e748\u67085\u65e5(\u91d1) 14:30\uff5e15:30<br \/>\n\u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e 534<\/p>\n<p>\u8b1b\u6f14\u8005\uff1a \u4e2d\u52d9 \u4f51\u6cbb (University of Oxford)<br \/>\n\u984c\u76ee\uff1a Best L1 Polynomial Approximation<\/p>\n<p>\u6982\u8981\uff1a<br \/>\nAn important observation in compressed sensing is the exact recovery of<br \/>\nan l0 minimizer to an underdetermined linear system via the l1<br \/>\nminimizer, given the knowledge that a sparse solution vector exists.<br \/>\nHere, we develop a continuous analogue of this observation and show that<br \/>\nthe best L1 and L0 polynomial approximants of a corrupted function<br \/>\n(continuous analogue of sparse vectors) are equivalent. We use this to<br \/>\nconstruct best L1 polynomial approximants of corrupted functions via<br \/>\nlinear programming. We also present a numerical algorithm for computing<br \/>\nbest L1 polynomial approximants to general continuous functions, and<br \/>\nobserve that compared with best L-infinity and L2 polynomial<br \/>\napproximants, the best L1 approximants tend to have error functions that<br \/>\nare more localized.<\/p>\n<p>This is joint work with Alex Townsend (MIT).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65e5\u6642\uff1a\u30002016\u5e748\u67085\u65e5(\u91d1) 14:30\uff5e15:30 \u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e 5&hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/comments?post=285"}],"version-history":[{"count":0,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/285\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/media?parent=285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/categories?post=285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/tags?post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}