{"id":5760,"date":"2024-11-22T11:08:05","date_gmt":"2024-11-22T17:08:05","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=5760"},"modified":"2024-11-22T11:08:05","modified_gmt":"2024-11-22T17:08:05","slug":"mn2d","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-2\/mn2d\/","title":{"rendered":"mn2d Secante"},"content":{"rendered":"\n<p>El m\u00e9todo de la Secante se utiliza en lugar del m\u00e9todo de Newton, cuando la derivada de la funci\u00f3n es complicada de obtener. B\u00e1sicamente es la misma expresi\u00f3n de Newton, s\u00f3lo que ahora se deben emplear dos valores iniciales y la f\u00f3rmula<\/p>\n\n\n\n<p>x3 = x2 \u2013 (fx2)(x2 \u2013 x1) \/ (fx2 \u2013 fx1)<\/p>\n\n\n\n<p>Los nuevos valores calculados sustituyen a los primeros y se repiten los c\u00e1lculos hasta hallar la ra\u00edz o funci\u00f3n f = 0. Esto es, x1 = x3, fx1 = fx3 y se repiten los c\u00e1lculos.<\/p>\n\n\n\n<p>Ejemplo. Resuelva por el m\u00e9todo de la secante para la funci\u00f3n<\/p>\n\n\n\n<p>f(x) = x^3 + 2x^2 \u2013 8x -4 con dos valores iniciales x1 = 1 y x2 = 2<\/p>\n\n\n\n<p>Soluci\u00f3n. Con estos valores iniciales fx1 = \u2013 9, fx2 = \u2013 4. Sustituyendo sucesivamente los c\u00e1lculos son<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x1<\/td><td>x2<\/td><td>f(x1)<\/td><td>f(x2)<\/td><td>x3<\/td><td>f(x3)<\/td><\/tr><tr><td>1<\/td><td>2<\/td><td>-9<\/td><td>-4<\/td><td>2.8<\/td><td>11.232<\/td><\/tr><tr><td>2.8<\/td><td>2<\/td><td>11.232<\/td><td>-4<\/td><td>2.21008403<\/td><td>-1.11663707<\/td><\/tr><tr><td>2.21008403<\/td><td>2<\/td><td>-1.11663707<\/td><td>-4<\/td><td>2.29144307<\/td><td>0.20158418<\/td><\/tr><tr><td>2.29144307<\/td><td>2<\/td><td>0.20158418<\/td><td>-4<\/td><td>2.27746017<\/td><td>-0.03324474<\/td><\/tr><tr><td>2.27746017<\/td><td>2<\/td><td>-0.03324474<\/td><td>-4<\/td><td>2.27978552<\/td><td>0.00556734<\/td><\/tr><tr><td>2.27978552<\/td><td>2<\/td><td>0.00556734<\/td><td>-4<\/td><td>2.27939665<\/td><td>-0.00092996<\/td><\/tr><tr><td>2.27939665<\/td><td>2<\/td><td>-0.00092996<\/td><td>-4<\/td><td>2.27946162<\/td><td>0.0001554<\/td><\/tr><tr><td>2.27946162<\/td><td>2<\/td><td>0.0001554<\/td><td>-4<\/td><td>2.27945076<\/td><td>-2.5968E-05<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>EJERCICIO.&nbsp;Utilizar Excel o Matlab para desarrollar una secuencia de c\u00e1lculo que permita calcular la ra\u00edz a trav\u00e9s de un programa.<\/p>\n\n\n\n<p>Soluci\u00f3n<\/p>\n\n\n\n<p><strong>Excel<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2019\/09\/secante1.png?w=750\" alt=\"\" class=\"wp-image-166\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2019\/09\/secante2.png?w=750\" alt=\"\" class=\"wp-image-167\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2019\/09\/secante3.png?w=750\" alt=\"\" class=\"wp-image-168\" \/><\/figure><\/div>\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2019\/09\/secante4.png?w=750\" alt=\"\" class=\"wp-image-169\" \/><\/figure><\/div>\n\n\n<p><strong>Matlab<\/strong><\/p>\n\n\n\n<p>p = [1 2 -8 -4]<\/p>\n\n\n\n<p>r = roots(p)<\/p>\n\n\n\n<p>r =<\/p>\n\n\n\n<p>-3.8201<br>2.2795<br>-0.4594<\/p>\n\n\n\n<div class=\"is-content-justification-center is-layout-flex wp-container-1 wp-block-buttons\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-2\/\">regresar<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>El m\u00e9todo de la Secante se utiliza en lugar del m\u00e9todo de Newton, cuando la derivada de la funci\u00f3n es complicada de obtener. B\u00e1sicamente es la misma expresi\u00f3n de Newton, s\u00f3lo que ahora se deben emplear dos valores iniciales y la f\u00f3rmula x3 = x2 \u2013 (fx2)(x2 \u2013 x1) \/ (fx2 \u2013 fx1) Los nuevos &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-2\/mn2d\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">mn2d Secante<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":417,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"_links":{"self":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5760"}],"collection":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/users\/123458"}],"replies":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/comments?post=5760"}],"version-history":[{"count":2,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5760\/revisions"}],"predecessor-version":[{"id":5775,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5760\/revisions\/5775"}],"up":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/417"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=5760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}