{"id":5819,"date":"2024-11-22T11:05:31","date_gmt":"2024-11-22T17:05:31","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=5819"},"modified":"2024-11-22T11:05:31","modified_gmt":"2024-11-22T17:05:31","slug":"mn4d","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/unidad-4\/mn4d\/","title":{"rendered":"mn4d Polinomio de Lagrange"},"content":{"rendered":"\n

El polinomio de Lagrange se genera con los datos tabulados y varios coeficientes. El polinomio de primer orden requiere dos puntos.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Para los datos<\/p>\n\n\n\n

x<\/td>1<\/td>2<\/td>3<\/td>4<\/td>5<\/td><\/tr>
y<\/td>8<\/td>15<\/td>22<\/td>30<\/td>38<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Primer orden<\/h2>\n\n\n\n

El polinomio de ajuste entre 2 y 4 se calcula como<\/p>\n\n\n\n

x0 = 2   dato 0 = 15, x1 = 4   dato 1 = 30\nL0 = (x - x1)\/(x0 - x1) = (x - 4)\/(2 - 4) = -0.5x + 2\nL1 = (x - x0)\/(x1 - x0) = (x - 2)\/(4 - 2) = 0.5x - 1\nf(x) = (-0.5x + 2)(15) + (0.5x - 1)(30) = 7.5x<\/pre>\n\n\n\n
x<\/td>2<\/td>3<\/td>4<\/td><\/tr>
f(x) = 7.5x<\/td>15<\/td>22.5<\/td>30<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
Segundo orden<\/h2>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n
Para los mismo puntos, esto es, 2 a 4.<\/p>\n\n\n\n
x0 = 2   dato 0 = 15, x1 = 3   dato 1 = 22, x2 = 4  dato 2 = 30\nL0 = (x-x1)(x-x2)\/(x0-x1)(x0-x2) = (x-3)(x-4)\/(2-3)(2-4) = 0.5x^2-3.5x+6\nL1 = (x-x0)(x-x2)\/(x1-x0)(x1-x2) = (x-2)(x-4)\/(3-2)(3-4) = -x^2+6x-8\nL2 = (x-x0)(x-x1)\/(x2-x0)(x2-x1) = (x-2)(x-3)\/(4-2)(4-3) = 0.5x^2-2.5x+3\n\nf(x) = (0.5x^2-3.5x+6)(15) + (-x^2+6x-8)(22) + (0.5x^2-2.5x+3)(30) \n     = 0.5x^2 +4.5x + 4<\/pre>\n\n\n\n
<\/p>\n\n\n\n
Ejemplo<\/h2>\n\n\n
\n
\"\"<\/figure><\/div>\n\n\n
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regresar<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
El polinomio de Lagrange se genera con los datos tabulados y varios coeficientes. El polinomio de primer orden requiere dos puntos. Para los datos x 1 2 3 4 5 y 8 15 22 30 38 Primer orden El polinomio de ajuste entre 2 y 4 se calcula como x0 = 2 dato 0 = … Contin\u00faa leyendo mn4d Polinomio de Lagrange<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":439,"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\/5819"}],"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=5819"}],"version-history":[{"count":4,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5819\/revisions"}],"predecessor-version":[{"id":5940,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5819\/revisions\/5940"}],"up":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/439"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=5819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}