{"id":4781,"date":"2015-02-19T08:34:11","date_gmt":"2015-02-19T07:34:11","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=4781"},"modified":"2015-02-19T08:34:11","modified_gmt":"2015-02-19T07:34:11","slug":"resena-qr-decomposition-in-isabellehol","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-qr-decomposition-in-isabellehol\/","title":{"rendered":"Rese\u00f1a: QR decomposition in Isabelle\/HOL"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle\/HOL sobre \u00e1lgebra lineal titulado <a href=\"http:\/\/bit.ly\/1Erc3cq\">QR decomposition<\/a>.<\/p>\n<p>Sus autores son <a href=\"http:\/\/www.unirioja.es\/cu\/jodivaso\">Jose Divas\u00f3n<\/a> y <a href=\"http:\/\/www.unirioja.es\/cu\/jearansa\">Jes\u00fas Aransay<\/a> (de la Universidad de la Rioja).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\n  QR decomposition is an algorithm to decompose a real matrix A into the product of two other matrices Q and R, where Q is orthogonal and R is invertible and upper triangular. The algorithm is useful for the least squares problem; i.e., the computation of the best approximation of an unsolvable system of linear equations. As a side-product, the Gram-Schmidt process has also been formalized. A refinement using immutable arrays is presented as well. The development relies, among others, on the AFP entry <a href=\"http:\/\/afp.sourceforge.net\/devel-entries\/Real_Impl.shtml\">Implementing field extensions of the form Q{sqrt(b)}<\/a>&#8221; by Ren\u00e9 Thiemann, which allows execution of the algorithm using symbolic computations. Verified code can be generated and executed using floats as well.\n<\/p><\/blockquote>\n<p>El trabajo se ha publicado la semana pasada en <a href=\"http:\/\/afp.sourceforge.net\/index.shtml\">The Archive of Formal Proofs<\/a><\/p>\n<p>El c\u00f3digo de las correspondientes teor\u00edas en Isabelle se encuentra <a href=\"http:\/\/bit.ly\/1ErcHGA\">aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle\/HOL sobre \u00e1lgebra lineal titulado QR decomposition. Sus autores son Jose Divas\u00f3n y Jes\u00fas Aransay (de la Universidad de la Rioja). Su resumen es QR decomposition is an algorithm to decompose a real matrix A into the product of two other matrices Q and R, where&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[100],"tags":[144,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4781"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=4781"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4781\/revisions"}],"predecessor-version":[{"id":4782,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/4781\/revisions\/4782"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=4781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=4781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=4781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}