{"id":54479,"date":"2006-08-09T00:00:00","date_gmt":"2006-08-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-el-problema-17-de-smale-teoria-de-la-interseccion-y-geometria-integral\/"},"modified":"2006-08-09T00:00:00","modified_gmt":"2006-08-09T00:00:00","slug":"sobre-el-problema-17-de-smale-teoria-de-la-interseccion-y-geometria-integral","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria\/sobre-el-problema-17-de-smale-teoria-de-la-interseccion-y-geometria-integral\/","title":{"rendered":"Sobre el problema 17 de smale: teor\u00eda de la intersecci\u00f3n y geometr\u00eda integral"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Carlos Beltran Alvarez <\/strong><\/h2>\n<p>En el a\u00f1o 2000, el ganador de la medalla fields stephen smale propuso 18 problemas de matem\u00e1ticas para el siglo xxi. El n\u00famero 17 de esos problemas pregunta sobre la existencia de un algoritmo que aproxime soluciones de sistemas de ecuaciones multivariados con coeficientes complejos, en un tiempo polilnomial en media en la talla del input. En esta tesis se expone la primera soluci\u00f3n probabil\u00edstica a este problema. Esto es, se describe un algoritmo con la propiedad de que, dado un sistema de ecuaciones polinomiales, encuentra una soluci\u00f3n aproximada en tiempo polinomial, aceptando una peque\u00f1a probabilidad de error que se puede ajustar en funci\u00f3n de las necesidades y recursos. Como paso previo a la resoluci\u00f3n de dicho problema, se introducen numerosos resultados intermedios que analizan el comportamiento promedio de las cantidades asociadas a la complejidad de resoluci\u00f3n, as\u00ed como a la estabilidad del problema.  en particular, se obtienen cotas de vol\u00famenes de tubos y de intersecci\u00f3n de tubos con variedades que permiten estimar mediante una t\u00e9cnica general todos los problemas del numero de condicionamiento lineal y no lineal, en un contexto ampliamente generalizado. los resultados son estudiados tanto desde un punto de vista de computaci\u00f3n continua como desde una perspectiva discreta, aportados para este \u00faltimo objetivo las cotas m\u00e1s finas conocidas hasta el momento de principios de transferencia de resultados continuos a discretos, principalmente en el caso de problemas definidos de modo proyectivo. Tambi\u00e9n se muestran otros resultados puramente geom\u00e9tricos y algebraicos con inter\u00e9s propio, y se estiman otras cantidades auxiliares de cierta relevancia, como la norma media de las soluciones de un sistema de ecuaciones polinomiales con coeficientes complejos.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre el problema 17 de smale: teor\u00eda de la intersecci\u00f3n y geometr\u00eda integral<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre el problema 17 de smale: teor\u00eda de la intersecci\u00f3n y geometr\u00eda integral <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Carlos Beltran Alvarez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Cantabria<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/09\/2006<\/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> Pardo Vasallo Luis Miguel<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Cuesta albertos Juan  Antonio <\/li>\n<li>gregorio Malajovich (vocal)<\/li>\n<li>dedieu Jean pierre (vocal)<\/li>\n<li> Morais san Miguel Jos\u00e9 enrique (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Carlos Beltran Alvarez En el a\u00f1o 2000, el ganador de la medalla fields stephen smale propuso 18 [&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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