| author | Alberto Bertogli
<albertito@blitiri.com.ar> 2010-09-10 03:23:49 UTC |
| committer | Alberto Bertogli
<albertito@blitiri.com.ar> 2010-09-10 03:23:49 UTC |
| parent | 974cc17258edbd8054d644f010d27d90c06fe089 |
| informe/resultados.lyx | +176 | -198 |
diff --git a/informe/resultados.lyx b/informe/resultados.lyx index b5d098d..6111f3f 100644 --- a/informe/resultados.lyx +++ b/informe/resultados.lyx @@ -1,10 +1,10 @@ -#LyX 1.6.7 created this file. For more info see http://www.lyx.org/ +#LyX 1.6.5 created this file. For more info see http://www.lyx.org/ \lyxformat 345 \begin_document \begin_header \textclass article \use_default_options true -\language english +\language spanish \inputencoding auto \font_roman default \font_sans default @@ -17,14 +17,17 @@ \graphics default \paperfontsize default +\spacing single \use_hyperref false \papersize default -\use_geometry false +\use_geometry true \use_amsmath 1 \use_esint 1 \cite_engine basic \use_bibtopic false \paperorientation portrait +\leftmargin 3cm +\rightmargin 3cm \secnumdepth 3 \tocdepth 3 \paragraph_separation indent @@ -36,7 +39,6 @@ \tracking_changes false \output_changes false \author "" -\author "" \end_header \begin_body @@ -51,20 +53,20 @@ Para analizar el comportamiento de los algoritmos y los metodos implementados, A continuacion se incluyen gráficos sobre los comportamientos más relevantes. \end_layout +\begin_layout Subsection +Comparativa general +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/babilonio-err-3d.png + filename ../plot/todos-result-p:51.png width 16cm \end_inset @@ -73,7 +75,7 @@ status open \begin_inset Caption \begin_layout Plain Layout - +Comparativa de resultados de distintos métodos, con precisión 51 \end_layout \end_inset @@ -82,8 +84,13 @@ status open \end_layout \begin_layout Plain Layout -Método babilonio con todas las combinaciones de iteraciones y precisión - de 0 a 50 con sus correspondientes errores +\begin_inset CommandInset label +LatexCommand label +name "Flo:comparativa de resultados, prec 51" + +\end_inset + + \end_layout \end_inset @@ -91,6 +98,15 @@ Método babilonio con todas las combinaciones de iteraciones y precisión \end_layout +\begin_layout Standard +Nuestro primer gráfico muestra el resultado obtenido por cada método conforme + aumenta la cantidad de iteraciones, en la máxima precisión. + Se grafican solo las implementaciones mas básicas por claridad, ya que + el objetivo es presentar visualmente el funcionamiento de cada método, + y las variantes no presentan comportamientos significativamente distinto, + como se verá en gráficos subsecuentes. +\end_layout + \begin_layout Standard \begin_inset Float figure placement H @@ -98,13 +114,9 @@ wide false sideways false status open -\begin_layout Plain Layout - -\end_layout - \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/babilonio-err-i:50.png + filename ../plot/todos-result-p:51-sin_binomial.png width 16cm \end_inset @@ -113,7 +125,14 @@ status open \begin_inset Caption \begin_layout Plain Layout -dsa +Detalle de la figura +\begin_inset CommandInset ref +LatexCommand ref +reference "Flo:comparativa de resultados, prec 51" + +\end_inset + + \end_layout \end_inset @@ -126,6 +145,12 @@ dsa \end_layout +\begin_layout Standard +Este detalle de la figura anterior permite apreciar con mas detalle como + convergen los métodos de fracciones continuas y babilonio, aun con la máxima + precisión. +\end_layout + \begin_layout Standard \begin_inset Float figure placement H @@ -133,13 +158,9 @@ wide false sideways false status open -\begin_layout Plain Layout - -\end_layout - \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/babilonio-err-map.png + filename ../plot/todos-err-p:51.png width 16cm \end_inset @@ -148,12 +169,20 @@ status open \begin_inset Caption \begin_layout Plain Layout -dsa +Error en los distintos métodos segun la iteración, con precisión fija en + 51 \end_layout \end_inset +\begin_inset CommandInset label +LatexCommand label +name "Flo:comparativa de error, prec:51" + +\end_inset + + \end_layout \end_inset @@ -161,20 +190,31 @@ dsa \end_layout +\begin_layout Standard +Aquí nuevamente se utiliza la máxima precisión para ilustrar la convergencia + de los distintos métodos conforme aumenta la cantidad de iteraciónes. + En este caso, nos concentramos en el error del resultado obtenido en cada + caso. + Utilizamos una escala logarítmica para el mismo, con el propósito de incrementa +r la legibilidad del gráfico. +\end_layout + +\begin_layout Standard +De ahora en mas graficaremos casi exclusivamente el error, por considerarlo + mas representativo a fines de la realización de un análisis comparativo + de los métodos. +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/babilonio-err-p:51-detalle.png + filename ../plot/todos-err-p:51-detalle.png width 16cm \end_inset @@ -183,7 +223,14 @@ status open \begin_inset Caption \begin_layout Plain Layout -dsa +Detalle de la figura +\begin_inset CommandInset ref +LatexCommand ref +reference "Flo:comparativa de error, prec:51" + +\end_inset + + \end_layout \end_inset @@ -196,20 +243,34 @@ dsa \end_layout +\begin_layout Standard +Este detalle de la figura anterior nos permite ver claramente la fuerte + diferencia en la convergencia de los tres métodos. + Mientras que el babilonio alcanza el mejor resultado en la 5ª iteración, + y el de fracciónes continuas en la 19ª, ambos estabilizandose, el método + binomial (en su variante decreciente, aunque como veremos en la sección + correspondiente, no hay diferencia significativa en este caso en ninguno + de las variantes) aproxima de forma extremadamente lenta. +\end_layout + +\begin_layout Subsection +Diferentes metodos de aproximación de la mantisa +\end_layout + +\begin_layout Subsection +Método Babilonio +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/babilonio-err-p:51.png + filename ../plot/babilonio-err-map.png width 16cm \end_inset @@ -236,15 +297,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-3d-detalle2.png + filename ../plot/babilonio-err-3d.png width 16cm \end_inset @@ -253,7 +310,7 @@ status open \begin_inset Caption \begin_layout Plain Layout -dsa + \end_layout \end_inset @@ -261,6 +318,11 @@ dsa \end_layout +\begin_layout Plain Layout +Método babilonio con todas las combinaciones de iteraciones y precisión + de 0 a 50 con sus correspondientes errores. +\end_layout + \end_inset @@ -271,15 +333,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-3d-detalle3.png + filename ../plot/babilonio-err-i:50.png width 16cm \end_inset @@ -306,15 +364,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-3d-detalle-alt.png + filename ../plot/babilonio-err-p:51.png width 16cm \end_inset @@ -341,15 +395,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-3d-detalle.png + filename ../plot/babilonio-err-p:51-detalle.png width 16cm \end_inset @@ -371,20 +421,20 @@ dsa \end_layout +\begin_layout Subsection +Método Binomial +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-3d.png + filename ../plot/binomial-err-i:100.png width 16cm \end_inset @@ -411,15 +461,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-i:algunas.png + filename ../plot/binomial-err-i:100-detalle.png width 16cm \end_inset @@ -446,15 +492,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-map.png + filename ../plot/binomial-err-p:15,17.png width 16cm \end_inset @@ -481,15 +523,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-p:algunos-detalle1.png + filename ../plot/binomial-err-p:51.png width 16cm \end_inset @@ -511,20 +549,20 @@ dsa \end_layout +\begin_layout Subsubsection +Binomial simple e incremental +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-p:algunos-detalle2.png + filename ../plot/binomial-err-map.png width 16cm \end_inset @@ -551,15 +589,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial_dec-err-p:algunos.png + filename ../plot/binomial-err-3d.png width 16cm \end_inset @@ -586,15 +620,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-3d-detalle2.png + filename ../plot/binomial-err-3d-detalle.png width 16cm \end_inset @@ -621,15 +651,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-3d-detalle.png + filename ../plot/binomial-err-3d-detalle2.png width 16cm \end_inset @@ -656,15 +682,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-3d.png + filename ../plot/binomial_dec-err-i:algunas.png width 16cm \end_inset @@ -686,20 +708,20 @@ dsa \end_layout +\begin_layout Subsubsection +Binomial decremental +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-i:100-detalle.png + filename ../plot/binomial_dec-err-map.png width 16cm \end_inset @@ -708,7 +730,7 @@ status open \begin_inset Caption \begin_layout Plain Layout -dsa + \end_layout \end_inset @@ -726,15 +748,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-i:100.png + filename ../plot/binomial_dec-err-3d.png width 16cm \end_inset @@ -761,15 +779,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-map.png + filename ../plot/binomial_dec-err-3d-detalle.png width 16cm \end_inset @@ -796,15 +810,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-p:15,17.png + filename ../plot/binomial_dec-err-3d-detalle-alt.png width 16cm \end_inset @@ -831,15 +841,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/binomial-err-p:51.png + filename ../plot/binomial_dec-err-3d-detalle2.png width 16cm \end_inset @@ -866,15 +872,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/fcont-err-3d.png + filename ../plot/binomial_dec-err-3d-detalle3.png width 16cm \end_inset @@ -901,15 +903,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/fcont-err-i:10.png + filename ../plot/binomial_dec-err-p:algunos-detalle1.png width 16cm \end_inset @@ -936,15 +934,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/fcont-err-map.png + filename ../plot/binomial_dec-err-p:algunos-detalle2.png width 16cm \end_inset @@ -971,15 +965,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/fcont-err-p:51-detalle.png + filename ../plot/binomial_dec-err-p:algunos.png width 16cm \end_inset @@ -1001,20 +991,20 @@ dsa \end_layout +\begin_layout Subsection +Método de fracciones contínuas +\end_layout + \begin_layout Standard \begin_inset Float figure placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/fcont-err-p:51.png + filename ../plot/fcont-err-map.png width 16cm \end_inset @@ -1041,15 +1031,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/todos-err-p:51-detalle.png + filename ../plot/fcont-err-3d.png width 16cm \end_inset @@ -1076,15 +1062,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/todos-err-p:51.png + filename ../plot/fcont-err-p:51.png width 16cm \end_inset @@ -1111,7 +1093,7 @@ dsa placement H wide false sideways false -status open +status collapsed \begin_layout Plain Layout @@ -1119,7 +1101,7 @@ status open \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/todos-result-p:51.png + filename ../plot/fcont-err-p:51-detalle.png width 16cm \end_inset @@ -1146,15 +1128,11 @@ dsa placement H wide false sideways false -status open - -\begin_layout Plain Layout - -\end_layout +status collapsed \begin_layout Plain Layout \begin_inset Graphics - filename ../plot-trunc/todos-result-p:51-sin_binomial.png + filename ../plot/fcont-err-i:10.png width 16cm \end_inset