{"id":1278,"date":"2017-09-18T14:59:46","date_gmt":"2017-09-18T18:59:46","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/bruceedwards\/?page_id=1278"},"modified":"2026-03-19T08:16:03","modified_gmt":"2026-03-19T12:16:03","slug":"papers","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/bruceedwards\/papers\/","title":{"rendered":"Papers"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Papers<\/h1>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Convergence proofs for root-finding algorithms<\/strong><\/h4>\n\n\n\n<p>Fixed point iteration is linearly convergent: <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1288\">Fixed Point<\/a><\/p>\n\n\n\n\n\n<p>Bisection is linearly convergent: <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1309\">Bisection<\/a><\/p>\n\n\n\n\n\n<p>Newton&#8217;s method is quadratically convergent:\u00a0 <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1312\">Newton<\/a><\/p>\n\n\n\n\n\n<p>Secant method convergence: <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1315\">Secant<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong> The Lagrange Interpolating Polynomial <\/strong><\/h4>\n\n\n\n<p>Generalized Rolle&#8217;s Theorem:  <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1334\"> GeneralRolle <\/a><\/p>\n\n\n\n\n\n<p>Lagrange Error Formula: <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1336\">LagrangeError<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong> The Trapezoidal Rule Error Formula <\/strong><\/h4>\n\n\n\n<p>Second Mean Value Theorem for Integrals: <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1343\">SecondMVThIntegrals<\/a><\/p>\n\n\n\n\n\n<p>Error Formula for the Trapezoidal Rule:<a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1344\">TrapError<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>The CORDIC algorithm<\/strong><\/h4>\n\n\n\n<p>How do calculators calculate? <a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1303\">paper<\/a><a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1303\">1<\/a><\/p>\n\n\n\n\n\n<p>How do calculators calculate trigonometric functions?<a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1298\">\u00a0paper<\/a><\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>The Implicit Function Theorem:\u00a0 <\/strong><a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1305\">implicit<\/a><\/h4>\n\n\n\n\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Cubic Equations: <\/strong><a href=\"https:\/\/people.clas.ufl.edu\/bruceedwards\/content-removed\/\" rel=\"attachment wp-att-1307\">cubic<\/a><\/h4>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":302,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1278","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/pages\/1278","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/users\/302"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/comments?post=1278"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/pages\/1278\/revisions"}],"predecessor-version":[{"id":1472,"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/pages\/1278\/revisions\/1472"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/bruceedwards\/wp-json\/wp\/v2\/media?parent=1278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}