{"id":5764,"date":"2024-11-22T11:03:06","date_gmt":"2024-11-22T17:03:06","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=5764"},"modified":"2024-11-22T11:03:06","modified_gmt":"2024-11-22T17:03:06","slug":"mn2f","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-2\/mn2f\/","title":{"rendered":"mn2f Punto Fijo"},"content":{"rendered":"\n<p>En la t\u00e9cnica de punto fijo se requiere despejar la variable x &nbsp;de alg\u00fan t\u00e9rmino de &nbsp;la funci\u00f3n inicial &nbsp;f(x) para tener la igualdad<\/p>\n\n\n\n<p>x = g(x)<\/p>\n\n\n\n<p>luego con un valor inicial de x &nbsp;se calcula &nbsp;el valor de la funci\u00f3n g(x) para obtener una nueva aproximaci\u00f3n de x. El c\u00e1lculo se repite hasta llegar al mismo valor de x<\/p>\n\n\n\n<p>Una ecuaci\u00f3n c\u00fabica como x^3 + 2x^2 \u2013 8x \u2013 4 puede despegar a la variable x en al menos tres opciones.<\/p>\n\n\n\n<p>a) del t\u00e9rmino lineal, &nbsp; x = (x^3 + 2x^2 \u2013 4) \/ 8<\/p>\n\n\n\n<p>b) del t\u00e9rmino cuadr\u00e1tico, &nbsp;x = (4x + 2 \u2013 x^3\/2 ) ^ (1\/2)<\/p>\n\n\n\n<p>c)&nbsp;del t\u00e9rmino c\u00fabico, &nbsp;x = (8x + 4 \u2013 2x^2 ) ^ (1\/3)<\/p>\n\n\n\n<p>&nbsp;Iniciando con x = 1, estos son los resultados.<\/p>\n\n\n\n<p>para a )<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>g1<\/td><td>fx<\/td><\/tr><tr><td>1<\/td><td>-0.125<\/td><td>-9<\/td><\/tr><tr><td>-0.125<\/td><td>1.43722427<\/td><td>-2.97070313<\/td><\/tr><tr><td>1.43722427<\/td><td>2.24841481<\/td><td>-8.39781695<\/td><\/tr><tr><td>2.24841481<\/td><td>2.28155251<\/td><td>-0.5100132<\/td><\/tr><tr><td>2.28155251<\/td><td>2.27930113<\/td><td>0.03512379<\/td><\/tr><tr><td>2.27930113<\/td><td>2.27946315<\/td><td>-0.00252538<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>para b )<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>g2<\/td><td>fx<\/td><\/tr><tr><td>1<\/td><td>11<\/td><td>-9<\/td><\/tr><tr><td>3.31662479<\/td><td>-5.94987437<\/td><td>27.9498744<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Al aparecer n\u00fameros negativos, se tiene que utilizar n\u00fameros complejos. Por ello, esta opci\u00f3n no se recomienda. Adem\u00e1s de que no converge a la soluci\u00f3n, dado que el valor de la funci\u00f3n en mayor en valor absoluto.<\/p>\n\n\n\n<p>para c )<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>g3<\/td><td>fx<\/td><\/tr><tr><td>1<\/td><td>2.15443469<\/td><td>-9<\/td><\/tr><tr><td>2.15443469<\/td><td>2.28639095<\/td><td>-1.95229985<\/td><\/tr><tr><td>2.286390955<\/td><td>2.27894845<\/td><td>0.11633941<\/td><\/tr><tr><td>2.278948451<\/td><td>2.27948842<\/td><td>-0.00841508<\/td><\/tr><tr><td>2.279488415<\/td><td>2.27944973<\/td><td>0.00060307<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>en a) y c) se obtiene el mismo valor de x = 2.2795<\/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>En la t\u00e9cnica de punto fijo se requiere despejar la variable x &nbsp;de alg\u00fan t\u00e9rmino de &nbsp;la funci\u00f3n inicial &nbsp;f(x) para tener la igualdad x = g(x) luego con un valor inicial de x &nbsp;se calcula &nbsp;el valor de la funci\u00f3n g(x) para obtener una nueva aproximaci\u00f3n de x. El c\u00e1lculo se repite hasta llegar &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-2\/mn2f\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">mn2f Punto Fijo<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":417,"menu_order":6,"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\/5764"}],"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=5764"}],"version-history":[{"count":2,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5764\/revisions"}],"predecessor-version":[{"id":5779,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5764\/revisions\/5779"}],"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=5764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}