{"id":240,"date":"2015-12-05T11:51:14","date_gmt":"2015-12-05T02:51:14","guid":{"rendered":"http:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/?p=240"},"modified":"2015-12-05T11:51:14","modified_gmt":"2015-12-05T02:51:14","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%85-1210","status":"publish","type":"post","link":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/2015\/12\/05\/%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%85-1210\/","title":{"rendered":"\u300c\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0\u300d\u30bb\u30df\u30ca\u30fc\u6848\u5185 (12\/10)"},"content":{"rendered":"<p>\u65e5\u6642 \uff1a 2015\u5e74 12\u670810\u65e5(\u6728) 17:30 \uff5e 18:30<\/p>\n<p>\u5834\u6240 \uff1a \u6771\u4eac\u5927\u5b66  \u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e 534\u53f7\u5ba4<br \/>\nhttp:\/\/www.u-tokyo.ac.jp\/campusmap\/cam01_04_15_j.<\/p>\n<p>\u8b1b\u6f14\u8005\uff1aJared Aurentz (University of Oxford)<\/p>\n<p>Part 1\u30bf\u30a4\u30c8\u30eb\uff1aFast algorithms for spectral differentiation matrices<br \/>\n\u8b1b\u6f14\u6982\u8981\uff1aRecently Olver and Townsend presented a fast spectral method<br \/>\nthat relies on bases of ultraspherical polynomials to give<br \/>\ndifferentiation matrices that are almost banded. The almost-banded<br \/>\nstructure allowed them to develop efficient algorithms for solving<br \/>\nceratin discretized systems in linear time. We show that one can also<br \/>\ndesign fast algorithms for standard spectral methods because the<br \/>\nunderlying matrices, though dense, have the same rank structure as those<br \/>\nof Olver and Townsend.<\/p>\n<p>Part 2 \u30bf\u30a4\u30c8\u30eb\uff1aKrylov methods for operators<br \/>\n\u8b1b\u6f14\u6982\u8981\uff1aIn this talk we will explore the convergence of Krylov methods<br \/>\nwhen used to solve $Lu = f$ where $L$ is an unbounded linear operator.<br \/>\nWe will show that for certain problems, methods like Conjugate Gradients<br \/>\nand GMRES still converge even though the spectrum of $L$ is unbounded. A<br \/>\ntheoretical justification for this behavior is given in terms of<br \/>\npolynomial approximation on unbounded domains.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65e5\u6642 \uff1a 2015\u5e74 12\u670810\u65e5(\u6728) 17:30 \uff5e 18:30 \u5834\u6240 \uff1a \u6771\u4eac\u5927\u5b66 \u5de5\u5b66\u90e8 1&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-240","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\/240","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=240"}],"version-history":[{"count":0,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/240\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/categories?post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}