{VERSION 2 3 "IBM INTEL NT" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 1 12 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 } 3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 7 264 1 {CSTYLE "" -1 -1 " " 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 256 43 "Minimi erung eines Fehlerpolynoms (septisch)" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 264 "" 0 "" {TEXT 290 69 "Theorie dazu unter http://www.nad irpoint.de/Dokumentenserver.html#SAW" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 257 39 "Dipl.- Ing. Bj\366rnstjerne Zindler, M.Sc." }}{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 60 "Erstellt: 20. August 2014 - Letzte Revision: 26. August 2014" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 106 "################################################## ########################################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 41 "Erstellen eines septischen Fehlerpolynoms" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 143 "expr1:=interp([3,5,6,8,11,12,14,16],[4,3,0,2,5,-2,-6,-10],x):expr 2:=interp([3,5,6,8,11,12,14,16],[4,2,1,-3,-4,-6,-9,-10],x):expr3:=expr 2-expr1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 174 "Grafische Darstellung des septischen Fe hlerpolynoms (ROT - erstes Interpolationspolynom, BLAU - zweites Inter polationspolynom, SCHWARZ - ergebender Betrag des Fehlerpolynoms)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 98 "plot([expr1,expr2,signum(expr3)*expr3],x=3..16,thic kness=2,color=[red,blue,black],numpoints=1000);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 29 "Sepa rierung der Koeffizienten" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "c[7]:=coeff(expr3,x, 7):c[6]:=coeff(expr3,x,6):c[5]:=coeff(expr3,x,5):c[4]:=coeff(expr3,x,4 ):c[3]:=coeff(expr3,x,3):c[2]:=coeff(expr3,x,2):c[1]:=coeff(expr3,x,1) :c[0]:=coeff(expr3,x,0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " #" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 59 "Versuch der Ermittlung von \+ m \374ber das \"Verk\374rzte Verfahren\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "equ1: =c[0]+c[2]*m^2+c[4]*m^4+c[6]*m^6:evalf(solve(equ1=0,m)):#plot(equ1,m=- 2..2,thickness=2,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 38 "Einzig rell e L\366sung ist ermittelt mit:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "m:=1.814458528; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 65 "Versuch der Ermittlung vom x[M] \374ber das \"Ausf \374hrliche Verfahren\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "# " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 31 "Definition der Restglieder R [n]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "R[7]:=c[7]:R[6]:=c[6]:R[5]:=7*c[7]*m^2+c[5 ]:R[4]:=5*c[6]*m^2+c[4]:R[3]:=7*c[7]*m^4+10/3*c[5]*m^2+c[3]:R[2]:=3*c[ 6]*m^4+2*c[4]*m^2+c[2]:R[1]:=c[7]*m^6+c[5]*m^4+c[3]*m^2+c[1]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 47 "Definition des Polynoms zur Ermittlung von x[M]" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 164 "equ2:=simplify(7*R[7]*x[M]^6+6*R[6]*x[M]^5+5*R[5]* x[M]^4+4*R[4]*x[M]^3+3*R[3]*x[M]^2+2*R[2]*x[M]^1+1*R[1]*x[M]^0):#plot( equ2,x[M]=0..15,thickness=2,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 47 "Ermitt lung aller potentieller L\366sungen f\374r x[M]" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(equ2=0,x[M]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 267 55 "Kontrolle der Art des Extremas \+ f\374r x[M] = 0,2106622856 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=.2106622856; m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0..7)-sum((x[M]-m)^i*c[i], i=0..7)):op(select(x->Im(x)=0,[solve(equ3=0,m)]));x:=x[M]:signum_expr_ 1:=signum(expr3):x:='x':equ4:=signum_expr_1*simplify(sum(i*(x[M]+m)^(i -1)*c[i],i=0..7)-sum(i*(x[M]-m)^(i-1)*c[i],i=0..7)):m:=1.814458528:x[M ]:=.2106622856:equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "# " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 85 "Der im Verk\374rzten Verfahr en ermittelte Wert f\374r \"m\" erscheint wieder, x[M] generiert " } {TEXT 270 4 "kein" }{TEXT 271 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 269 54 "Kontrolle der Art des Extremas f\374r x[M] = 4,747726013 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=4.747726013;m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0.. 7)-sum((x[M]-m)^i*c[i],i=0..7)):op(select(x->Im(x)=0,[solve(equ3=0,m)] ));x:=x[M]:signum_expr_1:=signum(expr3):x:='x':equ4:=signum_expr_1*sim plify(sum(i*(x[M]+m)^(i-1)*c[i],i=0..7)-sum(i*(x[M]-m)^(i-1)*c[i],i=0. .7)):m:=1.814458395:x[M]:=4.747726013:equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 85 "Der im Verk\374rzten Verfahren ermittelte Wert f\374r \"m\" erscheint wieder , x[M] generiert " }{TEXT 273 4 "kein" }{TEXT 274 8 " Minimum" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 54 "Kontrolle der Art des Extremas f\374r x[M] = 5,869206041 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=5.869206041;m:='m':equ3:=simplify(sum( (x[M]+m)^i*c[i],i=0..7)-sum((x[M]-m)^i*c[i],i=0..7)):op(select(x->Im(x )=0,[solve(equ3=0,m)]));x:=x[M]:signum_expr_1:=signum(expr3):x:='x':eq u4:=signum_expr_1*simplify(sum(i*(x[M]+m)^(i-1)*c[i],i=0..7)-sum(i*(x[ M]-m)^(i-1)*c[i],i=0..7)):m:=1.814457995:x[M]:=5.869206041:equ4<0;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 276 85 "Der im Verk\374rzten Verfahren ermittelte Wert f\374r \+ \"m\" erscheint wieder, x[M] generiert " }{TEXT 277 4 "kein" }{TEXT 278 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 279 54 "Kontrolle der Art des Extremas f \374r x[M] = 9,903165607 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=9.903165607;m: ='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0..7)-sum((x[M]-m)^i*c[i],i= 0..7)):op(select(x->Im(x)=0,[solve(equ3=0,m)]));x:=x[M]:signum_expr_1: =signum(expr3):x:='x':equ4:=signum_expr_1*simplify(sum(i*(x[M]+m)^(i-1 )*c[i],i=0..7)-sum(i*(x[M]-m)^(i-1)*c[i],i=0..7)):m:=1.814481600:x[M]: =9.903165607:equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" } }}{EXCHG {PARA 0 "" 0 "" {TEXT 280 85 "Der im Verk\374rzten Verfahren \+ ermittelte Wert f\374r \"m\" erscheint wieder, x[M] generiert " } {TEXT 281 4 "kein" }{TEXT 282 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 54 "Kontrolle der Art des Extremas f\374r x[M] = 13,01415382 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=13.01415382;m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0.. 7)-sum((x[M]-m)^i*c[i],i=0..7)):op(select(x->Im(x)=0,[solve(equ3=0,m)] ));x:=x[M]:signum_expr_1:=signum(expr3):x:='x':equ4:=signum_expr_1*sim plify(sum(i*(x[M]+m)^(i-1)*c[i],i=0..7)-sum(i*(x[M]-m)^(i-1)*c[i],i=0. .7)):m:=1.814459820:x[M]:=13.01415382:equ4>0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 284 96 "Der im Verk\374rzten Verfahren ermittelte Wert f\374r \"m\" erscheint wieder , x[M] generiert ein Minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 285 54 "Kontrolle der Art des \+ Extremas f\374r x[M] = 14,08014230 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]: =14.08014230;m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0..7)-sum((x[ M]-m)^i*c[i],i=0..7)):op(select(x->Im(x)=0,[solve(equ3=0,m)]));x:=x[M] :signum_expr_1:=signum(expr3):x:='x':equ4:=signum_expr_1*simplify(sum( i*(x[M]+m)^(i-1)*c[i],i=0..7)-sum(i*(x[M]-m)^(i-1)*c[i],i=0..7)):m:=1. 814458441:x[M]:=14.08014230:equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 286 85 "Der im Verk \374rzten Verfahren ermittelte Wert f\374r \"m\" erscheint wieder, x[M ] generiert " }{TEXT 287 4 "kein" }{TEXT 288 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 261 "" 0 "" {TEXT 289 84 "Das Fehlerpolynom ist minimiert an der Stelle x[m] = 13. 01415382 und m = 1,957238674" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "################ ###########################################Ende####################### ####################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" } }}}{MARK "1 3 0" 69 }{VIEWOPTS 1 1 0 1 1 1803 }