{"id":37892,"date":"1998-06-02T00:00:00","date_gmt":"1998-06-02T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/teoremas-de-convergencia-y-de-comparacion-para-particiones-y-multiparticiones\/"},"modified":"1998-06-02T00:00:00","modified_gmt":"1998-06-02T00:00:00","slug":"teoremas-de-convergencia-y-de-comparacion-para-particiones-y-multiparticiones","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/teoremas-de-convergencia-y-de-comparacion-para-particiones-y-multiparticiones\/","title":{"rendered":"Teoremas de convergencia y de comparacion para particiones y multiparticiones"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Mar\u00eda  Del Carmen Perea Marco <\/strong><\/h2>\n<p>Para la resoluci\u00f3n del sistema lineal ax=b, donde a es en general un operador acotado no singular en un espacio de banach, x es el vector de inc\u00f3gnitas y b es un vector dado, es bastante usual considerar el esquema iterativo secuencial asociado a una partici\u00f3n a=m &#8211; n, con m no singular.  en esta memoria se presentan condiciones necesarias y suficientes para que el radio espectral del operador de iteraci\u00f3n m elevado -1n sea estrictamente menor que uno, o lo que es equivalente, que el esquema iterativo secuencial converja a la soluci\u00f3n \u00fanica del sistema ax=b, dependiendo del tipo de partici\u00f3n considerada: regular, no negativa, d\u00e9bil no negativa del primer tipo, d\u00e9bil no negativa del segundo tipo, d\u00e9bil del primer tipo, d\u00e9bil del segundo tipo, p-regular, d\u00e9bil definida no negativa del primer tipo y d\u00e9bil definida no negativa del segundo tipo. Dadas dos particiones a= m sub1 &#8211; n sub1 = m sub2 &#8211; n sub2 del operador a tambi\u00e9n se ablecen condiciones que permite comparar el valor del radio espectral de los respectivos operadores de iteraci\u00f3n de cada una de ellas para los distintos tipos de particiones antes mencionadas. Adem\u00e1s se introducen una serie de relaciones entre las distintas condiciones de comparaci\u00f3n presentadas. Para aquellas condiciones de comparaci\u00f3n en las que aparecen operadores adjuntos, se considera que se trabaja en un espacio de hilbert en lugar de un espacio de banach. Lo mismo ocurre para las condiciones de convergencia y comparaci\u00f3n de particiones p-regulares y d\u00e9biles definidas no negativas del primer y del segundo tipo.  por otra parte, para el caso particular en el que a sea una matriz se establecen condiciones necesarias y suficientes de convergencia y de comparaci\u00f3n del esquema iterativo paralelo asociado a una multipartici\u00f3n (m subl, n subl, e subl) elevado p, sub l=1, donde para l=1&#8230;P, a=m subl &#8211; n subl es una partici\u00f3n de a, e subl igual 0 es una matriz diagonal y       e subp= i.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Teoremas de convergencia y de comparacion para particiones y multiparticiones<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Teoremas de convergencia y de comparacion para particiones y multiparticiones <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Mar\u00eda  Del Carmen Perea Marco <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Alicante<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 06\/02\/1998<\/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>Joan Josep Climent Coloma<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: rafael Bru Garc\u00eda <\/li>\n<li>b. Szyld daniel (vocal)<\/li>\n<li>Jos\u00e9 Mas mar\u00ed (vocal)<\/li>\n<li>Francisco Marcellan espa\u00f1ol (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Mar\u00eda Del Carmen Perea Marco Para la resoluci\u00f3n del sistema lineal ax=b, donde a es en general [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[19166,1191,126,16191,31239],"tags":[98900,4781,16886,31235,98899,15793],"class_list":["post-37892","post","type-post","status-publish","format-standard","hentry","category-alicante","category-analisis-numerico","category-matematicas","category-metodos-iterativos","category-resolucion-de-ecuaciones-lineales","tag-b-szyld-daniel","tag-francisco-marcellan-espanol","tag-joan-josep-climent-coloma","tag-jose-mas-mari","tag-maria-del-carmen-perea-marco","tag-rafael-bru-garcia"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/37892","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=37892"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/37892\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=37892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=37892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=37892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}