{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 228 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 262 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 265 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 1 18 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 270 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 272 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 275 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 278 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 280 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 284 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 285 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 290 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 291 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 295 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 296 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 297 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 300 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 301 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 302 "" 1 14 0 0 208 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 303 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 } {PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output " -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 265 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 266 41 "(4) Estimaci\363n del error y cambio de paso" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 264 56 "Ejerci cio 04-11 (del EXAMEN EXTRAORDINARIO de 01JUL05)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 74 "Para comparar dos m\351to dos de paso variable, que denotaremos por m1 y m2, " }}{PARA 4 "" 0 " " {TEXT -1 77 "se integra un problema test y se comparan los resultado s num\351ricos obtenidos " }}{PARA 4 "" 0 "" {TEXT -1 20 "con los dos \+ m\351todos." }}{PARA 4 "" 0 "" {TEXT -1 50 "Para el primero, m1 , se emplean las tolerancias" }}{PARA 4 "" 0 "" {TEXT -1 4 " " } {XPPEDIT 18 0 "10^(-3)" "6#)\"#5,$\"\"$!\"\"" }{TEXT -1 6 " , " } {XPPEDIT 18 0 "10^(-6)" "6#)\"#5,$\"\"'!\"\"" }{TEXT -1 5 " , " } {XPPEDIT 18 0 "10^(-9)" "6#)\"#5,$\"\"*!\"\"" }{TEXT -1 5 " , " } {XPPEDIT 18 0 "10^(-12);" "6#)\"#5,$\"#7!\"\"" }{TEXT -1 3 " ;" }} {PARA 4 "" 0 "" {TEXT -1 53 "para ellas los n\372meros de evaluaciones de funci\363n son" }}{PARA 4 "" 0 "" {TEXT -1 27 " 192 , 882 , 3808 , 12426" }}{PARA 4 "" 0 "" {TEXT -1 25 "y se obtienen los errores" }} {PARA 4 "" 0 "" {TEXT -1 91 " 0.102646532 10^(-1) , 0.028463542 10^( -5) , 0.185225052 10^(-8) , 0.253251780 10^(-9) , " }}{PARA 4 "" 0 "" {TEXT -1 36 "Para m2 se emplean las tolerancias" }}{PARA 4 "" 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "10^(-3)" "6#)\"#5,$\"\"$!\"\"" } {TEXT -1 6 " , " }{XPPEDIT 18 0 "10^(-4)" "6#)\"#5,$\"\"%!\"\"" } {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 53 "para ellas los n\372me ros de evaluaciones de funci\363n son" }}{PARA 4 "" 0 "" {TEXT -1 60 " 180 , 308 , 524 , 816 , 1332 , 2264 , 3896 , 6824 , 11932" }}{PARA 4 "" 0 "" {TEXT -1 25 "y se obtienen los errores" }}{PARA 4 "" 0 "" {TEXT -1 91 " 0.120075671 10^(-1) , 0.224069086 10^(-2) , 0.29345327 0 10^(-3) , 0.325178066 10^(-4) , " }}{PARA 4 "" 0 "" {TEXT -1 91 " \+ 0.397930221 10^(-5) , 0.436613469 10^(-6) , 0.445225052 10^(-7) , 0.45 5563685 10^(-8) , " }}{PARA 4 "" 0 "" {TEXT -1 39 " 0.473519591 10^( -9) " }}{PARA 4 "" 0 "" {TEXT -1 86 "Se puede deducir \+ de los datos anteriores con qu\351 orden est\341n funcionando los m \351todos ?" }}{PARA 4 "" 0 "" {TEXT -1 46 "Cu\341l es el que tiene me jor comportamiento ? " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r estart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "interface(labeli ng=false):" }}}{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 trace 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 257 15 "Variables lista" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "lista1eval:=[0,0,0,0]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "lista1erro:=[0,0,0,0]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "lista1logeval:=[0,0,0,0]:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "lista1logerro:=[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 "lista2erro:=[0 ,0,0,0,0,0,0,0,0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "lista 2logeval:=[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 " " {TEXT 258 11 "Datos de m1" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 39 "lista1eval:=[192 , 882 , 3808 , 12426]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "lista1erro:=[ 0.102646532 * 10^(-1) , 0.028463542 * 10^(-5) , 0.185225052 * 10^(-8) , 0.253251780 * 10^(-9)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from \+ 1 to 4 do lista1logeval[i]:=log[10](lista1eval[i]): od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "for i from 1 to 4 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&$\"%$G#!\"$$\"%XHF&$\"%!e$F&$\"%%4%F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$!%*)>!\"$$!%YlF&$!%K()F&$!%'f*F&" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 260 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 69 "Gr\341ficas comparadas 'n\372mero de evaluaciones versus log[10] d el error'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "lista1grafb:=[ seq([lista1eval[i],lista1logerro[i]],i=1..4)]:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "gra1b1:=plot(lista1grafb,style=LINE):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra1b2:=plot(lista1grafb,sty le=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gr a1b3:=textplot([3908, -9.12,`m1`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "lista2grafb:=[seq([lista2eval[i],lista2logerro[i]],i= 1..9)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra2b1:=plot(lis ta2grafb,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gr a2b2:=plot(lista2grafb,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "gra2b3:=textplot([3908, -6.50,`m2`]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "display(gra1b1,gra1b2,gra1b3 ,gra2b1,gra2b2,gra2b3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6*-%'CURVESG6%7&7$$\"$#>\"\"!$!5MpOB0>dl))>!#>7$$\"$#))F* $!5oBa=Ld5rXlF-7$$\"%3QF*$!5B@#*=iu-IK()F-7$$\"&EC\"F*$!5W*Q7%[$\\Zkf* F--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*FD-%&STYLEG6#%%LINEG-F$6&F&F=-%'SYM BOLG6#%$BOXG-FF6#%&POINTG-%%TEXTG6$7$$\"%3RF*$!$7*!\"#Q#m16\"-F$6%7+7$ $\"$!=F*$!5)[Ri#yx\\a?>F-7$$\"$3$F*$!5jM9#ot0='\\EF-7$$\"$C&F*$!5A#4s0 n/hC`$F-7$$\"$;)F*$!59_;/Cc(yy[%F-7$$\"%K8F*$!5Ve0+!p2$>+aF-7$$\"%kAF* $!5OK)=e4(G!*fjF-7$$\"%'*QF*$!5L6&*Hp1/U^tF-7$$\"%CoF*$!5)Qku]F!4XT$)F -7$$\"&K>\"F*$!5wwjb:[?mC$*F-F=FE-F$6&FinF=FKFO-FS6$7$FV$!$]'FZQ#m2Ffn -%+AXESLABELSG6%Q!FfnFbr-%%FONTG6#%(DEFAULTG-%%VIEWG6$FfrFfr" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" "Curve 4" "Curve 5" "Curve 6" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 256 81 "Gr\341ficas comparadas 'log[10] d el n\372mero de evaluaciones versus log[10] del error'" }}}{EXCHG {PARA 4 "" 0 "" {TEXT 302 48 "Recordemos lo que ya sabemos de otros pr oblemas:" }{TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 294 92 "Hay un tipo d e gr\341ficas que sirve para comprobar el orden 'efectivo' de los m \351todos, o sea, " }}{PARA 4 "" 0 "" {TEXT 268 90 "el orden con que, \+ en la pr\341ctica, parecen comportarse. En estas gr\341ficas se debe p resentar" }}{PARA 4 "" 0 "" {TEXT 269 94 "en el eje de abscisas el log [10] del paso empleado y en el de ordenadas el log[10] del error. " }} {PARA 4 "" 0 "" {TEXT 270 90 "Entonces el aspecto de la gr\341fica se \+ aproxima a una recta (o se puede aproximar utilizando" }}{PARA 4 "" 0 "" {TEXT 271 91 "la regresi\363n lineal). La pendiente de esa recta es el orden con que se comporta el m\351todo. " }}{PARA 4 "" 0 "" {TEXT 272 59 "En efecto, si el m\351todo es de orden p , el error ser\341 \+ O(" }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 273 37 ") . Considera ndo que, aproximadamente" }}{PARA 4 "" 0 "" {TEXT 274 20 "se tiene E (h) = K " }{XPPEDIT 18 0 "h^p" "6#)%\"hG%\"pG" }{TEXT 275 78 " , resu lta que el cociente incremental (la pendiente aproximada de la recta) \+ " }}{PARA 4 "" 0 "" {TEXT 276 43 "entre dos puntos correspondientes a \+ pasos " }{XPPEDIT 18 0 "h[1]" "6#&%\"hG6#\"\"\"" }{TEXT 277 3 " < " } {XPPEDIT 18 0 "h[2]" "6#&%\"hG6#\"\"#" }{TEXT 278 5 " es " }}{PARA 4 "" 0 "" {TEXT 279 5 " " }{XPPEDIT 18 0 "(log[10] (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 280 89 "Esta pendiente se puede estudiar \+ cuando se utilizan los segmentos correspondientes a los " }}{PARA 4 " " 0 "" {TEXT 284 69 "menores valores de h , los mas representativos d el efecto del orden." }}{PARA 4 "" 0 "" {TEXT 281 101 "Algo semejante \+ ocurre cuando se presenta en el eje de abscisas el log[10] del numero de evaluaciones" }}{PARA 4 "" 0 "" {TEXT 285 97 "y en el de ordenadas el log[10] del error. Entonces tambi\351n el aspecto de la gr\341fica se aproxima " }}{PARA 4 "" 0 "" {TEXT 299 98 "a una recta (o se puede aproximar utilizando la regresi\363n lineal). Pero la pendiente de es a recta " }}{PARA 4 "" 0 "" {TEXT 300 91 "es ahora igual a menos el or den con que se comporta el m\351todo, debido a que en el cociente " }} {PARA 4 "" 0 "" {TEXT 301 39 "antes expuesto el denominador es ahora \+ " }}{PARA 4 "" 0 "" {TEXT 288 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 286 3 " = " }{XPPEDIT 18 0 "log[10] (m/h[2])-log[10] (m/h[1])" "6#,&-&%$logG6#\"#56#*&%\"mG\"\" \"&%\"hG6#\"\"#!\"\"F,-&F&6#F(6#*&F+F,&F.6#F,F1F1" }{TEXT 287 4 " = \+ " }}{PARA 4 "" 0 "" {TEXT 289 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 290 4 " = " }{XPPEDIT 18 0 "log[10] (h[1])-log[10] (h[2])" "6#,&-&%$logG6#\"#56#&%\"hG6#\"\"\"F--&F&6#F(6#&F+6#\"\"#!\"\"" } {TEXT 291 21 " " }}{PARA 4 "" 0 "" {TEXT 282 87 "e n el supuesto de que m es el n\372mero de evaluaciones por paso del \+ m\351todo en cuesti\363n." }}{PARA 4 "" 0 "" {TEXT 283 101 "Esta idea \+ se emplea especialmente cuando el m\351todo es de paso variable y se d esea averiguar su orden " }}{PARA 4 "" 0 "" {TEXT 292 104 "efectivo, y a que, entonces, no tiene sentido hablar del paso del m\351todo, pero \+ s\355 que lo tiene hablar de " }}{PARA 4 "" 0 "" {TEXT 293 42 "las eva luaciones realizadas por el mismo. " }}{PARA 4 "" 0 "" {TEXT 295 95 "Y esto es justamente lo que sucede en este caso en el que hay que compa rar con m\351todos de paso " }}{PARA 4 "" 0 "" {TEXT 296 97 "variable; por ello no emplearemos las gr\341ficas 'log[10] del paso versus log[ 10] del error' , que " }}{PARA 4 "" 0 "" {TEXT 297 106 "carecen ahora \+ de sentido, sino las gr\341ficas 'log[10] del n\372mero de evaluacione s versus log[10] del error'," }}{PARA 4 "" 0 "" {TEXT 298 70 "que son \+ las que ahora pueden servir para detectar el 'orden efectivo'." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "lista1grafb:=[seq([lista1logeval[i] ,lista1logerro[i]],i=1..4)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra1b1:=plot(lista1grafb,style=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra1b2:=plot(lista1grafb,style=POINT,symbol=BOX): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "gra1b3:=textplot([log[1 0](3908), -9.12,`m1`]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " lista2grafb:=[seq([lista2logeval[i],lista2logerro[i]],i=1..9)]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "gra2b1:=plot(lista2grafb,sty le=LINE):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "gra2b2:=plot(l ista2grafb,style=POINT,symbol=BOX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "gra2b3:=textplot([log[10](3908), -6.50,`m2`]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "display(gra1b1,gra1b2,gra1b3 ,gra2b1,gra2b2,gra2b3);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6*-%'CURVESG6%7&7$$\"5'3'\\NqG7I$G#!#>$!5MpOB0>dl))>F*7$$ \"57t>=8&eoa%HF*$!5oBa=Ld5rXlF*7$$\"5`tOCrRpp!e$F*$!5B@#*=iu-IK()F*7$$ \"5$Hi4x#\\8L%4%F*$!5W*Q7%[$\\Zkf*F*-%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"! FDFC-%&STYLEG6#%%LINEG-F$6&F&F<-%'SYMBOLG6#%$BOXG-FF6#%&POINTG-%%TEXTG 6$7$$\"59YNn/bX&>f$F*$!$7*!\"#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$$\"5))3D+pWKrwSF* $!5wwjb:[?mC$*F*F " 0 "" {MPLTEXT 1 0 73 "display(gra1b1,gra1b2,gra1b3,gra2b1,gra2b2,gra2b3,scaling='CONSTRAINE D');" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6+-%'CURVE SG6%7&7$$\"5'3'\\NqG7I$G#!#>$!5MpOB0>dl))>F*7$$\"57t>=8&eoa%HF*$!5oBa= Ld5rXlF*7$$\"5`tOCrRpp!e$F*$!5B@#*=iu-IK()F*7$$\"5$Hi4x#\\8L%4%F*$!5W* Q7%[$\\Zkf*F*-%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"!FDFC-%&STYLEG6#%%LINEG- F$6&F&F<-%'SYMBOLG6#%$BOXG-FF6#%&POINTG-%%TEXTG6$7$$\"59YNn/bX&>f$F*$! $7*!\"#Q#m16\"-F$6%7+7$$\"5)pgI.^]s_D#F*$!5)[Ri#yx\\a?>F*7$$\"5>EW/];2 b)[#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;DU w[N$F*$!5OK)=e4(G!*fjF*7$$\"5\"=zd1#[*=1f$F*$!5L6&*Hp1/U^tF*7$$\"5dhm% f\"=!RS$QF*$!5)Qku]F!4XT$)F*7$$\"5))3D+pWKrwSF*$!5wwjb:[?mC$*F*F " 0 "" {MPLTEXT 1 0 87 "pendm1:=evalf((lista1logerro[4]-lista1logerro[3])/(li sta1logeval[4]-lista1logeval[3]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%'pendm1G$!5iaHZ;:pT#o\"!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "pendm2:=evalf((lista2logerro[9]-lista2logerro[8])/(lista2logeval [9]-lista2logeval[8]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'pendm2G$ !5&=Fxe31o:0%!#>" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 58 "El orden efe ctivo de m1 es de 1.7 , el de m2 es de 4.1" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 261 37 "b) M\351todo con mejor comportami ento " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 97 "El m\351todo m1 parece tener algo mejor comportamiento al princi pio, pero, cuando se mira el orden" }}{PARA 0 "" 0 "" {TEXT 303 100 "( o sea, lo que sucede cuando el paso se convierte en peque\361o) result a claramente mejor el m\351todo m2" }}}}{MARK "0 3 0" 15 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }