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" } {XPPEDIT 18 0 "y/(4 t^2)" "6#*&%\"yG\"\"\"*&\"\"%F%*$%\"tG\"\"#F%!\"\" " }{TEXT -1 7 " , t " }{XPPEDIT 18 0 "epsilon" "6#%(epsilonG" } {TEXT -1 55 " [ 0.1 , 10 ] " }}{PARA 4 "" 0 "" {TEXT -1 78 "y se comparan los resultados num\351ric os con otros dos m\351todos, uno de ellos de " }}{PARA 4 "" 0 "" {TEXT -1 81 "paso variable, que denotaremos por m2 , y el otro de pas o fijo, que denotaremos " }}{PARA 4 "" 0 "" {TEXT -1 42 "por m3 . Par a m1 se emplearon los pasos" }}{PARA 4 "" 0 "" {TEXT 260 3 " " } {XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT -1 8 " = 0.5 ," } {TEXT 261 2 " " }{XPPEDIT 18 0 "1/2^2" "6#*&\"\"\"F$*$\"\"#F&!\"\"" } {TEXT -1 10 " = 0.25 , " }{XPPEDIT 18 0 "1/2^3" "6#*&\"\"\"F$*$\"\"#\" \"$!\"\"" }{TEXT -1 11 " = 0.125 , " }{XPPEDIT 18 0 "1/2^4" "6#*&\"\" \"F$*$\"\"#\"\"%!\"\"" }{TEXT -1 12 " = 0.0625 , " }{XPPEDIT 18 0 "1/2 ^5" "6#*&\"\"\"F$*$\"\"#\"\"&!\"\"" }{TEXT -1 12 " = 0.0313 , " } {XPPEDIT 18 0 "1/2^6" "6#*&\"\"\"F$*$\"\"#\"\"'!\"\"" }{TEXT -1 15 " = 0.0156 " }}{PARA 4 "" 0 "" {TEXT -1 66 "lo que signufica que los n\372meros de evaluaciones de funci\363n fueron" }}{PARA 4 "" 0 "" {TEXT -1 57 " 390 , 790 , 1580 , 3160 , 6330 , 12670 \+ " }}{PARA 4 "" 0 "" {TEXT -1 27 "y se obtuvieron los errores" }}{PARA 4 "" 0 "" {TEXT -1 90 " 0.107100612 10^(-1) , 0.324754737 10^(-4) , \+ 0.173265513 10^(-6) , 0.921034842 10^(-9) ," }}{PARA 4 "" 0 "" {TEXT -1 46 " 0.405803845 10^(-11) , 0.164174164 10^(-13)" }}{PARA 4 "" 0 "" {TEXT -1 38 "Para m2 se emplearon las tolerancias" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "10^(-3)" "6#)\"#5,$\"\"$!\"\"" }{TEXT -1 6 " , " }{XPPEDIT 18 0 "10^(-4)" "6#)\"#5,$\"\"%!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-5)" "6#)\"#5,$\"\"&!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-6)" "6#)\"#5,$\"\"'!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-7)" "6#)\"#5,$\"\"(!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-8)" "6#)\"#5,$\"\")!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-9)" "6#)\"#5,$\"\"*!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-10)" "6#)\"#5,$F$!\"\"" } {TEXT -1 5 " , " }{XPPEDIT 18 0 "10^(-11)" "6#)\"#5,$\"#6!\"\"" } {TEXT -1 3 " ;" }}{PARA 4 "" 0 "" {TEXT -1 56 "para ellas los n\372me ros de evaluaciones de funci\363n fueron" }}{PARA 4 "" 0 "" {TEXT -1 60 " 180 , 308 , 524 , 816 , 1332 , 2264 , 3896 , 6824 , 11932" }} {PARA 4 "" 0 "" {TEXT -1 27 "y se obtuvieron los errores" }}{PARA 4 " " 0 "" {TEXT -1 91 " 0.120075671 10^(-1) , 0.224069086 10^(-2) , 0.2 93453270 10^(-3) , 0.325178066 10^(-4) , " }}{PARA 4 "" 0 "" {TEXT -1 91 " 0.397930221 10^(-5) , 0.436613469 10^(-6) , 0.445225052 10^(-7) , 0.455563685 10^(-8) , " }}{PARA 4 "" 0 "" {TEXT -1 39 " 0.4735195 91 10^(-9) " }}{PARA 4 "" 0 "" {TEXT -1 44 "Finalmente , para m3 se emplearon los pasos" }}{PARA 4 "" 0 "" {TEXT 263 3 " \+ " }{XPPEDIT 18 0 "1/2" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT -1 8 " = 0.5 , " }{TEXT 264 2 " " }{XPPEDIT 18 0 "1/2^2" "6#*&\"\"\"F$*$\"\"#F&!\"\" " }{TEXT -1 10 " = 0.25 , " }{XPPEDIT 18 0 "1/2^3" "6#*&\"\"\"F$*$\"\" #\"\"$!\"\"" }{TEXT -1 11 " = 0.125 , " }{XPPEDIT 18 0 "1/2^4" "6#*&\" \"\"F$*$\"\"#\"\"%!\"\"" }{TEXT -1 12 " = 0.0625 , " }{XPPEDIT 18 0 "1 /2^5" "6#*&\"\"\"F$*$\"\"#\"\"&!\"\"" }{TEXT -1 12 " = 0.0313 , " } {XPPEDIT 18 0 "1/2^6" "6#*&\"\"\"F$*$\"\"#\"\"'!\"\"" }{TEXT -1 13 " = 0.0156 , " }{XPPEDIT 18 0 "1/2^7" "6#*&\"\"\"F$*$\"\"#\"\"(!\"\"" } {TEXT -1 11 " = 0.0078 ," }{TEXT 265 1 " " }{TEXT -1 4 " " }}{PARA 4 "" 0 "" {TEXT -1 28 "con n\372meros de evaluaciones " }}{PARA 4 "" 0 "" {TEXT -1 63 " 156 , 316 , 632 , 1264 , 2532 , 5068 , 10136 \+ " }}{PARA 4 "" 0 "" {TEXT -1 27 "y se obtuvieron los errore s" }}{PARA 4 "" 0 "" {TEXT -1 91 " 0.188422582 10^(-1) , 0.501136903 10^(-2) , 0.430771249 10^(-3) , 0.299114127 10^(-4) , " }}{PARA 4 "" 0 "" {TEXT -1 70 " 0.185532367 10^(-5) , 0.114097541 10^(-6) , 0.703 332178 10^(-8) " }}{PARA 4 "" 0 "" {TEXT -1 86 "Se puede deducir de los datos anteriores con qu\351 orden est\341n funcionando los m\351t odos ?" }}{PARA 4 "" 0 "" {TEXT -1 46 "Cu\341l es el que tiene mejor c omportamiento ? " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeling=fa lse):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(linalg):with(plots):" } }{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tr ace have been redefined and unprotected\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 15 "Variables lista" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "lista1eval:=[0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "lista1erro:=[0,0,0,0,0,0] :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lista1logeval:=[0,0,0, 0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lista1logerro:=[ 0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "lista2eval :=[0,0,0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "l ista2erro:=[0,0,0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lista2logeval:=[0,0,0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lista2logerro:=[0,0,0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "lista3eval:=[0,0,0,0,0,0,0]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "lista3erro:=[0,0,0,0,0,0,0]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "lista3logeval:=[0,0,0,0 ,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "lista3logerro:= [0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 11 "Datos de m1 " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "list a1eval:=[390 , 790 , 1580 , 3160 , 6330 , 12670]:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 161 "lista1erro:=[ 0.107100612 * 10^(-1) , 0.324 754737 * 10^(-4) , 0.173265513 * 10^(-6) , 0.921034842 * 10^(-9) , 0 .405803845 * 10^(-11) , 0.164174164 * 10^(-13)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 6 do lista1logeval[i]:=log[10 ](lista1eval[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "fo r i from 1 to 6 do lista1logerro[i]:=log[10](lista1erro[i]): od:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "evalf(lista1logeval,4);evalf (lista1logerro,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7($\"%\"f#!\"$$ \"%(*GF&$\"%)>$F&$\"%*\\$F&$\"%,QF&$\"%-TF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7($!%q>!\"$$!%)[%F&$!%hnF&$!%O!*F&$!%R6!\"#$!%y8F/" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 266 11 "Datos de m2" }{MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "lista2eval:=[180 , 308 , 5 24 , 816 , 1332 , 2264 , 3896 , 6824 , 11932]:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 228 "lista2erro:=[0.120075671 * 10^(-1) , 0.224069 086 * 10^(-2) , 0.293453270 * 10^(-3) , 0.325178066 * 10^(-4) , 0.3979 30221 * 10^(-5) , 0.436613469 * 10^(-6) , 0.445225052 * 10^(-7) , 0.45 5563685 * 10^(-8) , 0.473519591 * 10^(-9)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 9 do lista2logeval[i]:=log[10](lis ta2eval[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i f rom 1 to 9 do lista2logerro[i]:=log[10](lista2erro[i]): od:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "evalf(lista2logeval,4);evalf (lista2logerro,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7+$\"%bA!\"$$\"% )[#F&$\"%>FF&$\"%6HF&$\"%CJF&$\"%aLF&$\"%!f$F&$\"%LQF&$\"%wSF&" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7+$!%@>!\"$$!%]EF&$!%KNF&$!%)[%F&$!%+a F&$!%gjF&$!%^tF&$!%T$)F&$!%D$*F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 11 "Datos de m3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "lista3eval:=[156 , 316 , 632 , 1264 , 2532 , 5068 , 1 0136]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "lista3erro:=[0.1 88422582 * 10^(-1) , 0.501136903 * 10^(-2) , 0.430771249 * 10^(-3) , 0 .299114127 * 10^(-4) , 0.185532367 * 10^(-5) , 0.114097541 * 10^(-6 ) , 0.703332178 * 10^(-8)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 7 do lista3logeval[i]:=log[10](lista3eval[i]): od: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 7 do li sta3logerro[i]:=log[10](lista3erro[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "evalf(lista3logeval,4);evalf(lista3logerro,4);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7)$\"%$>#!\"$$\"%*\\#F&$\"%+GF&$\"%,JF &$\"%.MF&$\"%/PF&$\"%0SF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7)$!%D " 0 "" {MPLTEXT 1 0 60 "lista1grafa: =[seq([lista1eval[i],lista1logerro[i]],i=1..6)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra1a1:=plot(lista1grafa,style=LINE):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra1a2:=plot(lista1grafa,sty le=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "gr a1a3:=textplot([1.209e+004, -12.95,`m1`]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 60 "lista2grafa:=[seq([lista2eval[i],lista2logerro[i]], i=1..9)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra2a1:=plot(l ista2grafa,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " gra2a2:=plot(lista2grafa,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 44 "gra2a3:=textplot([1.158e+004, -8.642,`m2`]): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "lista3grafa:=[seq([list a3eval[i],lista3logerro[i]],i=1..7)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra3a1:=plot(lista3grafa,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra3a2:=plot(lista3grafa,style=POIN T,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "gra3a3:=t extplot([9552, -7.183,`m3`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "display(gra1a1,gra1a2,gra1a3,gra2a1,gra2a2,gra2a3,gra3a1,gra3a2, gra3a3);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6--%'C URVESG6%7(7$$\"$!R\"\"!$!5%G6[#\\Z!3-(>!#>7$$\"$!zF*$!5e'*R!>a]W%)[%F- 7$$\"%!e\"F*$!5TQG.CryGhnF-7$$\"%gJF*$!5kv#)[[SRsN!*F-7$$\"%IjF*$!5M=z LB%Qo\"R6!#=7$$\"&qE\"F*$!5yxyGl=&p%y8FB-%'COLOURG6&%$RGBG$\"#5!\"\"$F *F*FO-%&STYLEG6#%%LINEG-F$6&F&FH-FQ6#%&POINTG-%'SYMBOLG6#%$BOXG-%%TEXT G6$7$$\"%47\"\"\"$!%&H\"!\"#Q#m16\"-F$6%7+7$$\"$!=F*$!5)[Ri#yx\\a?>F-7 $$\"$3$F*$!5jM9#ot0='\\EF-7$$\"$C&F*$!5A#4s0n/hC`$F-7$$\"$;)F*$!59_;/C c(yy[%F-7$$\"%K8F*$!5Ve0+!p2$>+aF-7$$\"%kAF*$!5OK)=e4(G!*fjF-7$$\"%'*Q F*$!5L6&*Hp1/U^tF-7$$\"%CoF*$!5)Qku]F!4XT$)F-7$$\"&K>\"F*$!5wwjb:[?mC$ *F-FHFP-F$6&FeoFHFVFY-Fhn6$7$$\"%e6F]o$!%U')!\"$Q#m2Fbo-F$6%7)7$$\"$c \"F*$!5Toy#f#\\q'[s\"F-7$$\"$;$F*$!5Mb/'f_hV+I#F-7$$\"$K'F*$!5Ah-#e0H` dO$F-7$$\"%k7F*$!5?OR&))\\2jT_%F-7$$\"%KDF*$!5C^m/r9.eJdF-7$$\"%o]F*$! 5dTN1G:PsUpF-7$$\"&O,\"F*$!5)Hf8=G^RG:)F-FHFP-F$6&F`sFHFVFY-Fhn6$7$$\" %_&*F*$!%$=(F\\sQ#m3Fbo-%+AXESLABELSG6%Q!FboFav-%%FONTG6#%(DEFAULTG-%% VIEWG6$FevFev" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7 " "Curve 8" "Curve 9" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 257 81 "Gr\341f icas comparadas 'log[10] del n\372mero de evaluaciones versus log[10] \+ del error'" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 274 55 "Recordemos lo que \+ ya dijimos en el problema precedente:" }}{PARA 4 "" 0 "" {TEXT 301 92 "Hay un tipo de gr\341ficas que sirve para comprobar el orden 'efectiv o' de los m\351todos, o sea, " }}{PARA 4 "" 0 "" {TEXT 275 90 "el orde n con que, en la pr\341ctica, parecen comportarse. En estas gr\341fica s se debe presentar" }}{PARA 4 "" 0 "" {TEXT 276 94 "en el eje de absc isas el log[10] del paso empleado y en el de ordenadas el log[10] del \+ error. " }}{PARA 4 "" 0 "" {TEXT 277 90 "Entonces el aspecto de la gr \341fica se aproxima a una recta (o se puede aproximar utilizando" }} {PARA 4 "" 0 "" {TEXT 278 91 "la regresi\363n lineal). La pendiente de esa recta es el orden con que se comporta el m\351todo. " }}{PARA 4 " " 0 "" {TEXT 279 59 "En efecto, si el m\351todo es de orden p , el er ror ser\341 O(" }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 280 37 " ) . Considerando que, aproximadamente" }}{PARA 4 "" 0 "" {TEXT 281 20 "se tiene E(h) = K " }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 282 78 " , resulta que el cociente incremental (la pendiente aproxima da de la recta) " }}{PARA 4 "" 0 "" {TEXT 283 43 "entre dos puntos cor respondientes a pasos " }{XPPEDIT 18 0 "h[1]" "6#&%\"hG6#\"\"\"" } {TEXT 284 3 " < " }{XPPEDIT 18 0 "h[2]" "6#&%\"hG6#\"\"#" }{TEXT 285 5 " es " }}{PARA 4 "" 0 "" {TEXT 286 5 " " }{XPPEDIT 18 0 "(log[1 0] (E(h[2))-log[10] (E(h[1])))/(log[10] (h[2])-log[10] (h[1]))" "6#*&, &-&%$logG6#\"#56#-%\"EG6#&%\"hG6#\"\"#\"\"\"-&F'6#F)6#-F,6#&F/6#F2!\" \"F2,&-&F'6#F)6#&F/6#F1F2-&F'6#F)6#&F/6#F2F;F;" }{TEXT -1 4 " = " } {XPPEDIT 18 0 "(log[10] (K)+p*log[10](h[2])-log[10] (K)-p*log[10](h[1] ))/(log[10] (h[2])-log[10] (h[1]))" "6#*&,*-&%$logG6#\"#56#%\"KG\"\"\" *&%\"pGF,-&F'6#F)6#&%\"hG6#\"\"#F,F,-&F'6#F)6#F+!\"\"*&F.F,-&F'6#F)6#& F46#F,F,F;F,,&-&F'6#F)6#&F46#F6F,-&F'6#F)6#&F46#F,F;F;" }{TEXT -1 24 " = p " }}{PARA 4 "" 0 "" {TEXT 287 89 "Esta pendien te se puede estudiar cuando se utilizan los segmentos correspondientes a los " }}{PARA 4 "" 0 "" {TEXT 291 69 "menores valores de h , los m as representativos del efecto del orden." }}{PARA 4 "" 0 "" {TEXT 288 101 "Algo semejante ocurre cuando se presenta en el eje de abscisas e l log[10] del numero de evaluaciones" }}{PARA 4 "" 0 "" {TEXT 292 97 " y en el de ordenadas el log[10] del error. Entonces tambi\351n el aspe cto de la gr\341fica se aproxima " }}{PARA 4 "" 0 "" {TEXT 306 98 "a u na recta (o se puede aproximar utilizando la regresi\363n lineal). Per o la pendiente de esa recta " }}{PARA 4 "" 0 "" {TEXT 307 91 "es ahora igual a menos el orden con que se comporta el m\351todo, debido a que en el cociente " }}{PARA 4 "" 0 "" {TEXT 308 39 "antes expuesto el de nominador es ahora " }}{PARA 4 "" 0 "" {TEXT 295 5 " " }{XPPEDIT 18 0 "log[10] (eval(h[2]))-log[10] (eval(h[1]))" "6#,&-&%$logG6#\"#56# -%%evalG6#&%\"hG6#\"\"#\"\"\"-&F&6#F(6#-F+6#&F.6#F1!\"\"" }{TEXT 293 3 " = " }{XPPEDIT 18 0 "log[10] (m/h[2])-log[10] (m/h[1])" "6#,&-&%$lo gG6#\"#56#*&%\"mG\"\"\"&%\"hG6#\"\"#!\"\"F,-&F&6#F(6#*&F+F,&F.6#F,F1F1 " }{TEXT 294 4 " = " }}{PARA 4 "" 0 "" {TEXT 296 12 " = " } {XPPEDIT 18 0 "log[10](m)-log[10] (h[2])-log[10](m)+log[10] (h[1])" "6 #,*-&%$logG6#\"#56#%\"mG\"\"\"-&F&6#F(6#&%\"hG6#\"\"#!\"\"-&F&6#F(6#F* F4-&F&6#F(6#&F16#F+F+" }{TEXT 297 4 " = " }{XPPEDIT 18 0 "log[10] (h[ 1])-log[10] (h[2])" "6#,&-&%$logG6#\"#56#&%\"hG6#\"\"\"F--&F&6#F(6#&F+ 6#\"\"#!\"\"" }{TEXT 298 21 " " }}{PARA 4 "" 0 "" {TEXT 289 87 "en el supuesto de que m es el n\372mero de evaluacione s por paso del m\351todo en cuesti\363n." }}{PARA 4 "" 0 "" {TEXT 290 101 "Esta idea se emplea especialmente cuando el m\351todo es de paso \+ variable y se desea averiguar su orden " }}{PARA 4 "" 0 "" {TEXT 299 104 "efectivo, ya que, entonces, no tiene sentido hablar del paso del \+ m\351todo, pero s\355 que lo tiene hablar de " }}{PARA 4 "" 0 "" {TEXT 300 42 "las evaluaciones realizadas por el mismo. " }}{PARA 4 " " 0 "" {TEXT 302 95 "Y esto es justamente lo que sucede en este caso e n el que hay que comparar con m\351todos de paso " }}{PARA 4 "" 0 "" {TEXT 303 97 "variable; por ello no emplearemos las gr\341ficas 'log[1 0] del paso versus log[10] del error' , que " }}{PARA 4 "" 0 "" {TEXT 304 106 "carecen ahora de sentido, sino las gr\341ficas 'log[10] del n \372mero de evaluaciones versus log[10] del error'," }}{PARA 4 "" 0 " " {TEXT 305 70 "que son las que ahora pueden servir para detectar el ' orden efectivo'." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "lista1g rafb:=[seq([lista1logeval[i],lista1logerro[i]],i=1..6)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra1b1:=plot(lista1grafb,style=LINE ):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra1b2:=plot(lista1gr afb,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "gra1b3:=textplot([3.999, -11.78,`m1`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "lista2grafb:=[seq([lista2logeval[i],lista2logerr o[i]],i=1..9)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra2b1:= plot(lista2grafb,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra2b2:=plot(lista2grafb,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "gra2b3:=textplot([3.938, -9.505,`m2 `]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "lista3grafb:=[seq([ lista3logeval[i],lista3logerro[i]],i=1..7)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra3b1:=plot(lista3grafb,style=LINE):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra3b2:=plot(lista3grafb,sty le=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "gr a3b3:=textplot([3.877, -6.701,`m3`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "display(gra1b1,gra1b2,gra1b3,gra2b1,gra2b2,gra2b3,gra 3b1,gra3b2,gra3b3);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6--%'CURVESG6%7(7$$\"5l?*\\Eqgk5f#!#>$!5%G6[#\\Z!3-(>F*7$ $\"5!G9W!H\"4Fw*GF*$!5e'*R!>a]W%)[%F*7$$\"5KiAW&p3d')>$F*$!5TQG.CryGhn F*7$$\"5%=QS=E3(o*\\$F*$!5kv#)[[SRsN!*F*7$$\"5C5bt,5PS,QF*$!5M=zLB%Qo \"R6!#=7$$\"56MTM)[hwF5%F*$!5yxyGl=&p%y8FA-%'COLOURG6&%$RGBG$\"#5!\"\" $\"\"!FOFN-%&STYLEG6#%%LINEG-F$6&F&FG-FQ6#%&POINTG-%'SYMBOLG6#%$BOXG-% %TEXTG6$7$$\"%**R!\"$$!%y6!\"#Q#m16\"-F$6%7+7$$\"5)pgI.^]s_D#F*$!5)[Ri #yx\\a?>F*7$$\"5>EW/];2b)[#F*$!5jM9#ot0='\\EF*7$$\"58lEP)pGJ$>FF*$!5A# 4s0n/hC`$F*7$$\"5n9hQve,p6HF*$!59_;/Cc(yy[%F*7$$\"5>E#GM[A/X7$F*$!5Ve0 +!p2$>+aF*7$$\"57#QB;DUw[N$F*$!5OK)=e4(G!*fjF*7$$\"5\"=zd1#[*=1f$F*$!5 L6&*Hp1/U^tF*7$$\"5dhm%f\"=!RS$QF*$!5)Qku]F!4XT$)F*7$$\"5))3D+pWKrwSF* $!5wwjb:[?mC$*F*FGFP-F$6&FeoFGFVFY-Fhn6$7$$\"%QRF]o$!%0&*F]oQ#m2Fbo-F$ 6%7)7$$\"5qfhWN)fCJ>#F*$!5Toy#f#\\q'[s\"F*7$$\"5%=QS=E3(o*\\#F*$!5Mb/' f_hV+I#F*7$$\"5O,&Q#Gyqr+GF*$!5Ah-#e0H`dO$F*7$$\"5*3iOYR2Z<5$F*$!5?OR& ))\\2jT_%F*7$$\"5G\\<`M,PY.MF*$!5C^m/r9.eJdF*7$$\"5:t.9@1m$[q$F*$!5dTN 1G:PsUpF*7$$\"5n#\\Qv=gme+%F*$!5)Hf8=G^RG:)F*FGFP-F$6&F_sFGFVFY-Fhn6$7 $$\"%xQF]o$!%,nF]oQ#m3Fbo-%+AXESLABELSG6%Q!FboF`v-%%FONTG6#%(DEFAULTG- %%VIEWG6$FdvFdv" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 " display(gra1b1,gra1b2,gra1b3,gra2b1,gra2b2,gra2b3,gra3b1,gra3b2,gra3b3 ,scaling='CONSTRAINED');" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6.-%'CURVESG6%7(7$$\"5l?*\\Eqgk5f#!#>$!5%G6[#\\Z!3-(>F*7$ $\"5!G9W!H\"4Fw*GF*$!5e'*R!>a]W%)[%F*7$$\"5KiAW&p3d')>$F*$!5TQG.CryGhn F*7$$\"5%=QS=E3(o*\\$F*$!5kv#)[[SRsN!*F*7$$\"5C5bt,5PS,QF*$!5M=zLB%Qo \"R6!#=7$$\"56MTM)[hwF5%F*$!5yxyGl=&p%y8FA-%'COLOURG6&%$RGBG$\"#5!\"\" $\"\"!FOFN-%&STYLEG6#%%LINEG-F$6&F&FG-FQ6#%&POINTG-%'SYMBOLG6#%$BOXG-% %TEXTG6$7$$\"%**R!\"$$!%y6!\"#Q#m16\"-F$6%7+7$$\"5)pgI.^]s_D#F*$!5)[Ri #yx\\a?>F*7$$\"5>EW/];2b)[#F*$!5jM9#ot0='\\EF*7$$\"58lEP)pGJ$>FF*$!5A# 4s0n/hC`$F*7$$\"5n9hQve,p6HF*$!59_;/Cc(yy[%F*7$$\"5>E#GM[A/X7$F*$!5Ve0 +!p2$>+aF*7$$\"57#QB;DUw[N$F*$!5OK)=e4(G!*fjF*7$$\"5\"=zd1#[*=1f$F*$!5 L6&*Hp1/U^tF*7$$\"5dhm%f\"=!RS$QF*$!5)Qku]F!4XT$)F*7$$\"5))3D+pWKrwSF* $!5wwjb:[?mC$*F*FGFP-F$6&FeoFGFVFY-Fhn6$7$$\"%QRF]o$!%0&*F]oQ#m2Fbo-F$ 6%7)7$$\"5qfhWN)fCJ>#F*$!5Toy#f#\\q'[s\"F*7$$\"5%=QS=E3(o*\\#F*$!5Mb/' f_hV+I#F*7$$\"5O,&Q#Gyqr+GF*$!5Ah-#e0H`dO$F*7$$\"5*3iOYR2Z<5$F*$!5?OR& ))\\2jT_%F*7$$\"5G\\<`M,PY.MF*$!5C^m/r9.eJdF*7$$\"5:t.9@1m$[q$F*$!5dTN 1G:PsUpF*7$$\"5n#\\Qv=gme+%F*$!5)Hf8=G^RG:)F*FGFP-F$6&F_sFGFVFY-Fhn6$7 $$\"%xQF]o$!%,nF]oQ#m3Fbo-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6%Q! FboFdv-%%FONTG6#%(DEFAULTG-%%VIEWG6$FhvFhv" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 35 "a) Orden efectivo de los m\351todos " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm1:=evalf((lista1logerro [6]-lista1logerro[5])/(lista1logeval[6]-lista1logeval[5]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pendm1G$!56K99c(em.%z!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm2:=evalf((lista2logerro[9]-lis ta2logerro[8])/(lista2logeval[9]-lista2logeval[8]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pendm2G$!5&=Fxe31o:0%!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm3:=evalf((lista3logerro[7]-lista3logerro[6] )/(lista3logeval[7]-lista3logeval[6]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pendm3G$!5=<]o!fm<*>S!#>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 271 66 "El orden efectivo de m1 es de 8 . Los de m2 y m3 son de 4 ." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 37 "b) M \351todo con mejor comportamiento " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 269 81 "El m\351todo m1 parece tener mejor c omportamiento de cara al error cuando el paso " }}{PARA 0 "" 0 "" {TEXT 270 88 "se hace adecuadamente peque\361o. Adem\341s est\341 lo q ue hemos dicho del orden de los m\351todos. " }}}}{MARK "0 3 0" 15 } {VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }