{"id":106,"date":"2019-04-26T09:50:41","date_gmt":"2019-04-26T12:50:41","guid":{"rendered":"http:\/\/clsap.dcce.ibilce.unesp.br\/?page_id=106"},"modified":"2020-10-15T19:54:17","modified_gmt":"2020-10-15T22:54:17","slug":"mesmerize","status":"publish","type":"page","link":"https:\/\/clsap.dcce.ibilce.unesp.br\/","title":{"rendered":""},"content":{"rendered":"<div class=\"entry\">\n\n\n<p><p style=\"text-align: left;\">This site contains the paper \u201cAn efficient algorithm for the classical least squares approximation\u201d, co-authored by Dimitar K. Dimitrov and Louren\u00e7o L. Peixoto, and accepted for publication in SIAM Journal on Scientific Computing, as well as the related MATLAB codes.<\/p><\/p>\n\n\n\n<p><p style=\"text-align: left;\">The image of the green valley and the blue river below is in fact the outcome of the algorithm for the 10<sup>8<\/sup> green pieces of data <span class=\"wp-katex-eq\" data-display=\"false\">f(x_j) = e^{x_j} \\sin 12x_j + \\delta_{10^8}<\/span>, where <span class=\"wp-katex-eq\" data-display=\"false\"> x_j = -1+(2j-1)\/N<\/span> and <span class=\"wp-katex-eq\" data-display=\"false\"> \\delta_{10^8} <\/span> returns normally distributed pseudorandom numbers by MATLAB, and the blue river is the approximate solution of degree 12 of the Classical Least Squares Approximation Problem.<\/p><\/p>\n\n\n\n<div class=\"wp-block-image\">\r\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-259 aligncenter\" src=\"https:\/\/clsap.dcce.ibilce.unesp.br\/wp-content\/uploads\/2019\/04\/Captura-de-Tela-2019-04-29-\u00e0s-20.19.23-1-1024x682.png\" alt=\"\" width=\"430\" height=\"287\" srcset=\"https:\/\/clsap.dcce.ibilce.unesp.br\/wp-content\/uploads\/2019\/04\/Captura-de-Tela-2019-04-29-\u00e0s-20.19.23-1-1024x682.png 1024w, https:\/\/clsap.dcce.ibilce.unesp.br\/wp-content\/uploads\/2019\/04\/Captura-de-Tela-2019-04-29-\u00e0s-20.19.23-1-300x200.png 300w, https:\/\/clsap.dcce.ibilce.unesp.br\/wp-content\/uploads\/2019\/04\/Captura-de-Tela-2019-04-29-\u00e0s-20.19.23-1-768x512.png 768w, https:\/\/clsap.dcce.ibilce.unesp.br\/wp-content\/uploads\/2019\/04\/Captura-de-Tela-2019-04-29-\u00e0s-20.19.23-1.png 1942w\" sizes=\"auto, (max-width: 430px) 100vw, 430px\" \/><\/figure>\r\n<\/div>\n\n\n\n<p>&nbsp;<\/p>\n\n\n<\/div>","protected":false},"excerpt":{"rendered":"<p>This site contains the paper \u201cAn efficient algorithm for the classical least squares approximation\u201d, co-authored by Dimitar K. Dimitrov and Louren\u00e7o L. Peixoto, and accepted for publication in SIAM Journal on Scientific Computing, as well as the related MATLAB codes. The image of the green valley and the blue river below is in fact the &#8230;<\/p>\n","protected":false},"author":1,"featured_media":253,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-106","page","type-page","status-publish","has-post-thumbnail"],"_links":{"self":[{"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/pages\/106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=106"}],"version-history":[{"count":34,"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/pages\/106\/revisions"}],"predecessor-version":[{"id":445,"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/pages\/106\/revisions\/445"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=\/wp\/v2\/media\/253"}],"wp:attachment":[{"href":"https:\/\/clsap.dcce.ibilce.unesp.br\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}