{"id":22943,"date":"2018-03-09T09:13:19","date_gmt":"2018-03-09T09:13:19","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/aplicaciones-de-la-interpolacion-polinomica-clasica-en-algebra-computacional\/"},"modified":"2018-03-09T09:13:19","modified_gmt":"2018-03-09T09:13:19","slug":"aplicaciones-de-la-interpolacion-polinomica-clasica-en-algebra-computacional","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/alcala\/aplicaciones-de-la-interpolacion-polinomica-clasica-en-algebra-computacional\/","title":{"rendered":"Aplicaciones de la interpolaci\u00f3n polin\u00f3mica cl\u00e1sica en \u00e1lgebra computacional"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Ana Marco Garc\u00eda <\/strong><\/h2>\n<p>Muchos problemas de \u00e1lgebra computacional resultan intratables debido a que requieren demasiado tiempo y espacio para su resoluci\u00f3n. Este es el motivo por el cual la elaboraci\u00f3n de algoritmos que disminuyan estos requerimientos es un elemento esencial del \u00e1lgebra computacional.  en eta memoria presentamos un nuevo enfoque basado en el uso de la interpolaci\u00f3n cl\u00e1sica que nos permite desarrollar algoritmos eficientes para resolver algunos problemas habituales en \u00e1lgebra computacional.  nuestro m\u00e9todo har\u00e1 uso de la interpolaci\u00f3n de lagrange y aprovechar\u00e1 la estructura del sistema lineal asociado al problema de interpolaci\u00f3n para obtener algoritmos con un alto grado de paralelismo intr\u00ednseco, los cuales reducen en gran medida el coste de espacio y tiempo necesario para resolver un problema dado.  nuestros algoritmos tienen car\u00e1cter determin\u00edstico, es decir no poseen etapas probabil\u00edsticas, y son adecuados para el caso denso y para problemas que involucran coeficientes reales no racionales. El uso de la interpolaci\u00f3n nos permite reducir aquellos c\u00e1lculos en los que intervienen s\u00edmbolos a c\u00e1lculos que \u00fanicamente involucran n\u00fameros.  en el cap\u00edtulo 1 se presentan las herramientas b\u00e1sicas que se usar\u00e1n en el resto de los cap\u00edtulos: la interpolaci\u00f3n, las resultantes y la descomposici\u00f3n en valores singulares (svd).  en el segundo cap\u00edtulo se aborda el problema de la implicitaci\u00f3n de curvas mediante el c\u00e1lculo eficiente de la resultante de sylvester o de b\u00e9zout, dejando para el tercero la implicitaci\u00f3n de superficies haciendo uso de la resultante de macaulay.  estos resultados se extienden en el cap\u00edtulo 4 al c\u00e1lculo de determinantes de matrices con elementos polin\u00f3micos, problema que surge, adem\u00e1s de en la implicitaci\u00f3n, en otras \u00e1reas del \u00e1lgebra computacional .  el cap\u00edtulo 5 se dedica al estudio de la intersecci\u00f3n de curvas algebraicas planas. En este caso, la eficiencia del algoritmo residir\u00e1 t<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Aplicaciones de la interpolaci\u00f3n polin\u00f3mica cl\u00e1sica en \u00e1lgebra computacional<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Aplicaciones de la interpolaci\u00f3n polin\u00f3mica cl\u00e1sica en \u00e1lgebra computacional <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Ana Marco Garc\u00eda <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Alcal\u00e1<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 14\/05\/2003<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Jos\u00e9 Javier Mart\u00ednez Fern\u00e1ndez De Las Heras<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Juan Llovet verdugo <\/li>\n<li>Mar\u00eda cruz L\u00f3pez de silanes busto (vocal)<\/li>\n<li>laureano Gonzalez-vega (vocal)<\/li>\n<li>Jos\u00e9 Mar\u00eda Franco Garc\u00eda (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Ana Marco Garc\u00eda Muchos problemas de \u00e1lgebra computacional resultan intratables debido a que requieren demasiado tiempo y [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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