{"id":25199,"date":"2003-05-09T00:00:00","date_gmt":"2003-05-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/quasi-interpolantes-spline-discretos-de-norma-casi-ma%c2%adnima-teoria-y-aplicaciones\/"},"modified":"2003-05-09T00:00:00","modified_gmt":"2003-05-09T00:00:00","slug":"quasi-interpolantes-spline-discretos-de-norma-casi-ma%c2%adnima-teoria-y-aplicaciones","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/quasi-interpolantes-spline-discretos-de-norma-casi-ma%c2%adnima-teoria-y-aplicaciones\/","title":{"rendered":"Quasi-interpolantes spline discretos de norma casi m\u00ednima. teor\u00eda y aplicaciones"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Mar\u00eda Jos\u00e9 Ib\u00e1\u00f1ez P\u00e9rez <\/strong><\/h2>\n<p>Las funciones spline constituyen en la actualidad una herramienta b\u00e1sica en la teor\u00eda de aproximaci\u00f3n. Desde su introducci\u00f3n en la d\u00e9cada de los cuarenta del siglo pasado hasta la actualidad han ido ocupando parcelas cada vez m\u00e1s amplia, tanto cient\u00edficas como t\u00e9cnicas. Un problema b\u00e1sico en el que juegan un papel fundamental es la aproximaci\u00f3n de datos emp\u00edricos y de funciones de una y varias variables. La construcci\u00f3n de aproximantes spline puede llevarse a cabo de muy diversas formas, entre las que la m\u00e1s conocidas son la interpolaci\u00f3n y el ajuste por m\u00ednimos cuadrados. Son t\u00e9cnicas computacionalmente costosas, pues dan lugar a sistemas de ecuaciones lineales. esto es especialmente relevante cuando se aplica en varias variables. Los quasi-interpolantes spline surgen con el \u00e1nimo de conseguir buenos aproximantes con un coste moderado.  el procesamiento en tiempo real de gran cantidad de datos requiere que el aproximante spline sea construido conforme se dispone de la informaci\u00f3n, por lo que es necesario dise\u00f1ar m\u00e9todos de tipo local que, adem\u00e1s, tengan un alto orden de aproximaci\u00f3n.  el estudio es una variable y con nodos uniformemente espaciados se remonta a los trabajos de i.J. Schoenberg, quien consider\u00f3 como quasi-interpolantes series b-spline en cuyos coeficientes intervienen valores de funci\u00f3n o derivadas.  el siguiente paso fue emplear nodos no uniformemente espacios y los correspondientes b-splines. En lo que respecta al caso multivariado, para particiones regulares el papel del b-spline univariado pasa a ser desempe\u00f1ado por el box-spline o, en general, por b-splines (funciones polin\u00f3micas a trozos, de soporte compacto). Se utilizan valores de funci\u00f3n, de derivadas parciales o de valores integrales.  en esta memoria se estudian diversos problemas relativos a la construcci\u00f3n de quasi-interpolantes b-spline discretos en una y dos variables, a los que se exige, entre otras cosas, que sean exactos en<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Quasi-interpolantes spline discretos de norma casi m\u00ednima. teor\u00eda y aplicaciones<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Quasi-interpolantes spline discretos de norma casi m\u00ednima. teor\u00eda y aplicaciones <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Mar\u00eda Jos\u00e9 Ib\u00e1\u00f1ez P\u00e9rez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 05\/09\/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>Paul Sablonni\u00e9re<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Mar\u00eda no Gasca gonzalez <\/li>\n<li>driss Sbibih (vocal)<\/li>\n<li>Juan  Andr\u00e9s Ramirez gonzalez (vocal)<\/li>\n<li>daniel C\u00e1rdenas morales (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Mar\u00eda Jos\u00e9 Ib\u00e1\u00f1ez P\u00e9rez Las funciones spline constituyen en la actualidad una herramienta b\u00e1sica en la teor\u00eda [&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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