{"id":1170,"date":"2024-10-28T00:24:20","date_gmt":"2024-10-28T07:24:20","guid":{"rendered":"https:\/\/wp.math.berkeley.edu\/hades\/?p=1170"},"modified":"2024-11-21T17:24:28","modified_gmt":"2024-11-22T01:24:28","slug":"some-applications-of-interval-arithmetic","status":"publish","type":"post","link":"https:\/\/wp.math.berkeley.edu\/hades\/2024\/10\/28\/some-applications-of-interval-arithmetic\/","title":{"rendered":"Some applications of interval arithmetic"},"content":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0<strong>October 29th<\/strong>, will be at\u00a0<strong>2<\/strong><strong>:00pm<\/strong>\u00a0in\u00a0<strong>Room 740.<\/strong><\/p>\n<p><strong>Speaker:<\/strong><a href=\"https:\/\/tarheels.live\/jrowan\/\"> James Rowan<\/a><\/p>\n<p><strong>Abstract: <\/strong>Computers cannot do exact arithmetic with arbitrary real numbers. But as analysts, that shouldn&#8217;t bother us too much since we usually deal in inequalities; often, we only need upper and lower bounds. I will give an introduction to interval arithmetic and survey some ways to make rigorous use of numerics in PDE proofs. First, I will discuss an interval arithmetic version of Newton&#8217;s method for root-finding and illustrate its use to compute a threshold value of a physical parameter in a solitary water waves problem (from joint work with Lizhe Wan). Then I will discuss the use of interval arithmetic to &#8220;upgrade&#8221; approximate solutions to nearby exact solutions and give a survey of some recent developments in this area that have inspired some recent projects I have been working on.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The HADES seminar on Tuesday,\u00a0October 29th, will be at\u00a02:00pm\u00a0in\u00a0Room 740. Speaker: James Rowan Abstract: Computers cannot do exact arithmetic with arbitrary real numbers. But as analysts, that shouldn&#8217;t bother us too much since we usually deal in inequalities; often, we only need upper and lower bounds. I will give an introduction to interval arithmetic and [&hellip;]<\/p>\n","protected":false},"author":95,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[],"class_list":["post-1170","post","type-post","status-publish","format-standard","hentry","category-fall-2024"],"_links":{"self":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1170","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/users\/95"}],"replies":[{"embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/comments?post=1170"}],"version-history":[{"count":1,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1170\/revisions"}],"predecessor-version":[{"id":1171,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/posts\/1170\/revisions\/1171"}],"wp:attachment":[{"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/media?parent=1170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/categories?post=1170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wp.math.berkeley.edu\/hades\/wp-json\/wp\/v2\/tags?post=1170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}