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Bj\366rnstjerne Zin dler, M.Sc." }}{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 60 "Erstellt: 20. August 2014 - Letzte Revision: 27. August 2 014" }}{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 46 "Erstellen eines biquadratischen Fehlerpolynoms" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 113 "expr1:=interp([3,5,11,14,16],[4,-4,-8,-5,-3],x):ex pr2:=interp([3,5,11,14,16],[4,5,1,-5,-3],x):expr3:=expr2-expr1;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 179 "Grafische Darstellung des biquadratischen Fehlerpolynom s (ROT - erstes Interpolationspolynom, BLAU - zweites Interpolationspo lynom, 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,thickn ess=2,color=[red,blue,black],numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 29 "Separi erung der Koeffizienten" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "# " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "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 99 "equ1:= c[0]+c[2]*m^2+c[4]*m^4:evalf(solve(equ1=0,m)):#plot(equ1,m=-4..4,thick ness=2,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "# " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 38 "Einzig relle L\366sung ist e rmittelt mit:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "m:=3.874440646;" }}}{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 64 "R[4]:=c[4]:R[3]:=c[3]:R[2]:=2*c[4]*m^2+c[2]:R[1]:=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 Ermit tlung von x[M]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "equ2:=simplify(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]=-1..15,th ickness=2,numpoints=1000);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 47 "Ermittlung aller potenti eller 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] = -0,4 962114088" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 322 "x[M]:=-.4962114088;m:='m':equ3:=si mplify(sum((x[M]+m)^i*c[i],i=0..4)-sum((x[M]-m)^i*c[i],i=0..4)):op(sel ect(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..4 )-sum(i*(x[M]-m)^(i-1)*c[i],i=0..4)):m:=3.874440647:x[M]:=-.4962114088 :equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 85 "Der im Verk\374rzten Verfahren ermittelt e Wert f\374r \"m\" erscheint wieder, x[M] generiert " }{TEXT 269 4 "k ein" }{TEXT 270 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 276 52 "Kontrolle der Art des Ex tremas f\374r x[M] =8,095601879" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=8.095601 879;m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0..4)-sum((x[M]-m)^i*c [i],i=0..4)):op(select(x->Im(x)=0,[solve(equ3=0,m)]));x:=x[M]:signum_e xpr_1:=signum(expr3):x:='x':equ4:=signum_expr_1*simplify(sum(i*(x[M]+m )^(i-1)*c[i],i=0..4)-sum(i*(x[M]-m)^(i-1)*c[i],i=0..4)):m:=3.874440769 :x[M]:=8.095601879:equ4<0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 271 85 "Der im Verk\374rzten Ver fahren ermittelte Wert f\374r \"m\" erscheint wieder, x[M] generiert \+ " }{TEXT 272 4 "kein" }{TEXT 273 8 " Minimum" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 277 52 "Kontro lle der Art des Extremas f\374r x[M] =13,97753260" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "x[M]:=13.97753260;m:='m':equ3:=simplify(sum((x[M]+m)^i*c[i],i=0.. 4)-sum((x[M]-m)^i*c[i],i=0..4)):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..4)-sum(i*(x[M]-m)^(i-1)*c[i],i=0. .4)):m:=3.874440695:x[M]:=13.97753260:equ4>0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 "#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 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 261 "" 0 "" {TEXT 274 84 "Das Fehlerpolynom is t minimiert an der Stelle x[m] = 13,97753260 und m = 3,874440695" }}} {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 5 0" 39 }{VIEWOPTS 1 1 0 1 1 1803 }