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bb:=b; else aa:=b; bb:=a; fi;\n" }{MPLTEXT 1 0 50 " if f(a) *f(b)>0 then error \"bad interval\" fi;\n" }{MPLTEXT 1 0 20 " delta:= abs(a-b);\n" }{MPLTEXT 1 0 17 " for n to N do\n" }{MPLTEXT 1 0 21 " \+ ab:=(aa+bb)/2.;\n" }{MPLTEXT 1 0 22 " delta:=delta/2.;\n" } {MPLTEXT 1 0 16 " ff:=f(ab);\n" }{MPLTEXT 1 0 54 " if abs(ff)F/F$>F0F&C$>F/F&>F0F$@$2F:*&F8\"\"\"-F(6#F&FDYQ-bad~intervalF%>F 3-I$absGF*6#,&F$FDF&!\"\"?(F4FDFDF-I%trueGF*C'>F1*&,&F/FDF0FDFD$\"\"#F :FN>F3*&F3FDFUFN>F2-F(6#F1@$32-FK6#F2F,2F3F+OF1@%2F2F:>F/F1>F0F1I%FAIL GF*F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "halfing(-1,1,x ->x^2,1,1,10);" }}{PARA 8 "" 1 "" {TEXT 207 32 "Error, (in halfing) ba d interval" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "halfing(1.,2. ,x->2*sin(x)-x,0.0000001,100,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%F AILG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "debug(h alfing); halfing(1.,2.,x->2*sin(x)-x,0.000001,100,20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I(halfingG6\"" }}{PARA 9 "" 1 "" {TEXT 208 106 "\{-- > enter halfing, args = 1., 2., proc (x) options operator, arrow; 2*si n(x)-x end proc, 0.1e-5, 100, 20" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" \"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++ ++:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++]!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*t**)\\\\!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +++++:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++++]!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++++]i!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!)Q9Zq!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +++]P>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++D1>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++++DJ!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!) $)ys!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"++]i!*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+++]i:!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"('f`z!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++]i!*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"++vV)*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++]7y!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!(b$H[!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"++vV)*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+]7`%*=!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+++D1R!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"('ew:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+]7`%*=! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+vV['*=!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"++]7`>!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!(qFi\"! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+vV['*=!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+7y]&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++]i l(*!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!&(=A!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+7y]&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+J&>] *=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++D\"G)[!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"'Dux!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+J&> ]*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+sOE&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+]iSTC!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"'v wP!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+sOE&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+UdQ&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ DJq?7!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"'ex!#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!$;$!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+gW\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+1N\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+gJuO &*!#;" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%Z7!\"*" }}{PARA 9 "" 1 "" {TEXT 208 51 "<-- exit halfing (now at top level) = 1.895493506\}" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+1N\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "regulafalsi:=proc(a,b,f::procedure,eps,feps,N) l ocal aa,bb,ab,ff,fa,fb,delta,n;\n" }{MPLTEXT 1 0 55 " if f(a)<0 then \+ aa:=a; bb:=b; else aa:=b; bb:=a; fi;\n" }{MPLTEXT 1 0 25 " fa:=f(aa); fb:=f(bb);\n" }{MPLTEXT 1 0 46 " if fa*fb>0 then error \"bad interva l\" fi;\n" }{MPLTEXT 1 0 22 " delta:=abs(aa-bb);\n" }{MPLTEXT 1 0 17 " for n to N do\n" }{MPLTEXT 1 0 32 " ab:=aa-fa/(fb-fa)*(bb-aa);\n " }{MPLTEXT 1 0 16 " ff:=f(ab);\n" }{MPLTEXT 1 0 53 " if ff<0 th en delta:=abs(aa-ab); aa:=ab; fa:=ff;\n" }{MPLTEXT 1 0 48 " else de lta:=abs(ab-bb); bb:=ab; fb:=ff fi;\n" }{MPLTEXT 1 0 54 " if abs(ff )F/F$>F0F&C$>F/F&>F0F$>F3-F(6#F/>F4-F( 6#F0@$2F<*&F3\"\"\"F4FLYQ-bad~intervalF%>F5-I$absGF*6#,&F/FLF0!\"\"?(F 6FLFLF-I%trueGF*C&>F1,&F/FL*(F3FL,&F4FLF3FTFT,&F0FLF/FTFLFT>F2-F(6#F1@ %2F2FF5-FQ6#,&F/FLF1FT>F/F1>F3F2C%>F5-FQ6#,&F1FLF0FT>F0F1>F4F2@$32 -FQ6#F2F,2F5F+OF1I%FAILGF*F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "regulafalsi(-1,1,x->x^2,1,1,10);" }}{PARA 8 "" 1 "" {TEXT 207 36 "Error, (in regulafalsi) bad interval" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "regulafalsi(1.,2.,x->2*sin(x)-x,0.000001,100,7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+kU\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "secant:=proc(a,b,f::procedure,eps,feps,N) loc al aa,bb,ab,ff,fa,fb,delta,n;\n" }{MPLTEXT 1 0 17 " aa:=a; bb:=b;\n" }{MPLTEXT 1 0 25 " fa:=f(aa); fb:=f(bb);\n" }{MPLTEXT 1 0 22 " delta :=abs(aa-bb);\n" }{MPLTEXT 1 0 17 " for n to N do\n" }{MPLTEXT 1 0 32 " ab:=aa-fa/(fb-fa)*(bb-aa);\n" }{MPLTEXT 1 0 16 " ff:=f(ab); \n" }{MPLTEXT 1 0 37 " aa:=bb; fa:=fb; bb:=ab; fb:=ff;\n" }{MPLTEXT 1 0 24 " delta:=abs(aa-bb);\n" }{MPLTEXT 1 0 54 " if abs(ff)F/F$>F0F&>F3-F(6#F/>F4-F(6#F0>F5-I$absGF*6#,&F/\"\"\"F 0!\"\"?(F6FEFEF-I%trueGF*C*>F1,&F/FE*(F3FE,&F4FEF3FFFF,&F0FEF/FFFEFF>F 2-F(6#F1>F/F0>F3F4>F0F1>F4F2F@@$32-FB6#F2F,2F5F+OF1I%FAILGF*F%F%F%" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "secant(-1.,1.,x->x^2,10.,10 .,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "debug(secant); secant(-1.,1. ,x->x^2,10.,10.,2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I'secantG6\"" }} {PARA 9 "" 1 "" {TEXT 208 95 "\{--> enter secant, args = -1., 1., proc (x) options operator, arrow; x^2 end proc, 10., 10., 2" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\" \"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"# \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\"\"I)infinityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I)infinityG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\"\"I)inf inityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I)infinityG %*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I)infinityG%*prot ectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I*undefinedG%*protected G" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I*undefinedG%*protectedG" }} {PARA 11 "" 1 "" {XPPMATH 20 "$!\"\"I)infinityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I)infinityG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I*undefinedG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I*undefinedG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"I*undefinedG%*protectedG" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }}{PARA 9 "" 1 "" {TEXT 208 43 "<-- \+ exit secant (now at top level) = FAIL\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 " secant(-1.,0.5,x->x^2,0.01,100.,10);" }}{PARA 9 "" 1 "" {TEXT 208 100 "\{--> enter secant, args = -1., .5, proc (x) options operator, arrow; x^2 end proc, 0.1e-1, 100., 10" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!\" \"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#D!\" #" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"&!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#D!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*++++&!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+MLLLL! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+76666!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+++++5! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+MLLLL!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+76666!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mmmmm!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+,+++D!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+0++]i!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+MLLLL!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+76666!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+,+++D!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+0++]i!# 6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*LLLL)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+I9dG9!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Jj\"3/# !#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+,+++D!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+0++]i!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+I9dG9!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Jj\"3/#!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+r&G92\"!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*4444* !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3GYk#)!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+I9dG9!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Jj\"3/ #!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*4444*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3GYk#)!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*@0[>& !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ebbbb!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+c(>k3$!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*4444*! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+3GYk#)!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ebbbb!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+c(>k3$! #7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+KNNNN!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+keF[M!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+V11*=\" !#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ebbbb!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+c(>k3$!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+keF[M! #6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+V11*=\"!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+%pzs5#!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+x&fw7 #!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+w_$p_%!#8" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+keF[M!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+V11*= \"!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+x&fw7#!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+w_$p_%!#8" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+(G; 1K\"!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+u%*y:8!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+S>IJIJ " 0 "" {MPLTEXT 1 0 44 "secant(1.,2.,x->2*sin(x)-x,0.000001,100,10) ;" }}{PARA 9 "" 1 "" {TEXT 208 105 "\{--> enter secant, args = 1., 2., proc (x) options operator, arrow; 2*sin(x)-x end proc, 0.1e-5, 100, 1 0" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*q>%Ho!\" *" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*Y^S\"=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fY7!z\" !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*bH'>;!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"\"#\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*Y^S\"=! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fY7!z\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*bH'>;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*T`( )4#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\")5>S5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+f Y7!z\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*bH'>;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \")5>S5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\")*)e**)*!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\")5>S5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"(oUz'!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\& *=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"'1@U!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*= !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%c:!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*=!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F# " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"!\"*" }}{PARA 9 "" 1 "" {TEXT 208 50 "<-- exit secant (now at top level) = 1.895494267\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "debug(secant); secant(1.,2.,x->2*sin(x)-x,0.000001,10 0,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I'secantG6\"" }}{PARA 9 "" 1 "" {TEXT 208 104 "\{--> enter secant, args = 1., 2., proc (x) options op erator, arrow; 2*sin(x)-x end proc, 0.1e-5, 100, 6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#\"\" !" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*q>%Ho!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*Y^S\"=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\" \"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fY7!z\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*bH'>;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"# \"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*Y^S\"=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fY7!z\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*b H'>;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*T`()4#!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \")5>S5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+fY7!z\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*bH'>;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\")5>S5!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\")*)e**)*!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+[07*)=!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\")5>S5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f *=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"(oUz'!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\& *=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;[\"f*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!'Y!*o !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"'1@U! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+5F\\&* =!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%]D!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"%c:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F# " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+mU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=! \"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"!\"*" }}{PARA 9 "" 1 "" {TEXT 208 50 "<-- exit sec ant (now at top level) = 1.895494267\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Studen t[Calculus1][NewtonsMethodTutor](x-cos(x),0);" }}{PARA 8 "" 1 "" {TEXT 207 94 "Error, (in Student:-Calculus1:-NewtonsMethodTutor) the deriva tive is 0 after the 1st iteration" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "Newton:=proc(x0,f::procedure,fp::procedure,eps,feps,N ) local x,xx,delta,n;\n" }{MPLTEXT 1 0 9 "x:=x0; \n" }{MPLTEXT 1 0 15 "for n to N do\n" }{MPLTEXT 1 0 28 " xx:=x-evalf(f(x)/fp(x));\n" } {MPLTEXT 1 0 21 " delta:=abs(x-xx);\n" }{MPLTEXT 1 0 55 " if abs(f(x x))F0F$?(F3\"\"\"F7F. I%trueGF)C&>F1,&F0F7-I&evalfGF)6#*&-F'6#F0F7-F+FA!\"\"FC>F2-I$absGF)6# ,&F0F7F1FC@$32-FF6#-F'6#F1F-2F2F,OF1>F0F1I%FAILGF)F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Newton(1.,x->2*sin(x)-x,x->2*cos(x) -1,0.000001,100,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protecte dG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "debug(Newton); Newton (1.,x->2*sin(x)-x,x->2*cos(x)-1,0.000001,100,6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I'NewtonG6\"" }}{PARA 9 "" 1 "" {TEXT 208 155 "\{--> ente r Newton, args = 1., proc (x) options operator, arrow; 2*sin(x)-x end \+ proc, proc (x) options operator, arrow; 2*cos(x)-1 end proc, 0.1e-5, 1 00, 6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "$!+<1usu!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+<1us% )!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!+<1usu!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+iC&yW\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Cl 7&>#!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+iC&yW\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+\"QY^$p!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " $\"+R#yLa(!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+\"QY^$p!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+H-jj;!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+4f:,(*!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+H-jj; !\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+WZ?S$)!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Yv4'H)!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+WZ ?S$)!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+Mp3V\\!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"+5y6(R$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$ \"+Mp3V\\!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }} {PARA 9 "" 1 "" {TEXT 208 43 "<-- exit Newton (now at top level) = FAI L\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*protectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Newton(1.5,x->2*sin(x)-x,x->2*cos(x )-1,0.000001,100,6);" }}{PARA 9 "" 1 "" {TEXT 208 156 "\{--> enter New ton, args = 1.5, proc (x) options operator, arrow; 2*sin(x)-x end proc , proc (x) options operator, arrow; 2*cos(x)-1 end proc, 0.1e-5, 100, \+ 6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++#el2#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*+#eld !\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++#el2#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;m]5>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*%e^ g;!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;m]5>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+.?i&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\")8 Y)[\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+.?i&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+wU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 " $\"'Fx7!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+wU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU\\&*=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"*!\"*" }}{PARA 9 "" 1 "" {TEXT 208 50 "<-- exit Newton (now a t top level) = 1.895494267\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+nU \\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "modNewton:=pro c(x0,f::procedure,q,eps,feps,N) local x,xx,delta,n;\n" }{MPLTEXT 1 0 9 "x:=x0; \n" }{MPLTEXT 1 0 15 "for n to N do\n" }{MPLTEXT 1 0 24 " x x:=x-evalf(f(x)/q);\n" }{MPLTEXT 1 0 21 " delta:=abs(x-xx);\n" } {MPLTEXT 1 0 55 " if abs(f(xx))F/F$?(F2\"\"\"F6F-I%trueGF)C&>F0,&F/F6-I&evalfGF)6#*&-F'6#F/F6F*! \"\"FA>F1-I$absGF)6#,&F/F6F0FA@$32-FD6#-F'6#F0F,2F1F+OF0>F/F0I%FAILGF) F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "modNewton(2.,x->2 *sin(x)-x,2*cos(2.)-1,0.000001,100,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+QV\\&*=!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "debu g(modNewton); modNewton(1.5,x->2*sin(x)-x,2*cos(1.5)-1,0.000001,100,10 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "I*modNewtonG6\"" }}{PARA 9 "" 1 "" {TEXT 208 119 "\{--> enter modNewton, args = 1.5, proc (x) options op erator, arrow; 2*sin(x)-x end proc, -.8585255967, 0.1e-5, 100, 10" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"#:!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"++#el2#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*+#eld!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"++#el2#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+DWt&p\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*vP#3 Q!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+DWt&p\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+e5)>.#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"* LmCO$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+e5)>.#!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+f'\\8v\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"**RJ1G!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+f'\\8v\"!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+Vg5.?!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*%Qc!\"*" }}{PARA 11 " " 1 "" {XPPMATH 20 "$\"*3(4p>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\" +Y!y?)>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)3)o3=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*e**Qt\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)3)o3=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+#*y\"f'>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*/)Hs:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+#*y\"f'>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+>?7 E=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*tezR\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+>?7E=!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAI LG%*protectedG" }}{PARA 9 "" 1 "" {TEXT 208 46 "<-- exit modNewton (no w at top level) = FAIL\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*pro tectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 206 13 "*17.27. Egy p" }{TEXT 206 8 "\303\251" } {TEXT 206 27 "lda: a konvergencia rendje." }}{PARA 0 "" 0 "" {TEXT 201 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "quasiNewton:=proc (x0,f::procedure,fp::procedure,alpha,eps,feps,N) local x,xx,delta,n;\n " }{MPLTEXT 1 0 9 "x:=x0; \n" }{MPLTEXT 1 0 15 "for n to N do\n" } {MPLTEXT 1 0 34 " xx:=x-alpha*evalf(f(x)/fp(x));\n" }{MPLTEXT 1 0 21 " delta:=abs(x-xx);\n" }{MPLTEXT 1 0 55 " if abs(f(xx))F1F$?(F4\"\"\"F8F/I%trueGF )C&>F2,&F1F8*&F,F8-I&evalfGF)6#*&-F'6#F1F8-F+FC!\"\"F8FE>F3-I$absGF)6# ,&F1F8F2FE@$32-FH6#-F'6#F2F.2F3F-OF2>F1F2I%FAILGF)F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "debug(quasiNewton);\n" }{MPLTEXT 1 0 67 "quasiNewton(1,x->sin(x)^4,x->4*sin(x)^3*cos(x),1.,0.000001,100,1 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I,quasiNewtonG6\"" }}{PARA 9 "" 1 "" {TEXT 208 169 "\{--> enter quasiNewton, args = 1, proc (x) options operator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4*sin(x)^3*cos(x) end proc, 1., 0.1e-5, 100, 10" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)o![1h!#5" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+7$>N*Q!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+)o![1h!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+M3xcV! #5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+a)4(\\$ !#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+$\\vP;\"!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+T`*H>$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+`[Y mB!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*)[Il#)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+`[YmB!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+/i^X%!#5" }}{PARA 11 "" 1 " " {XPPMATH 20 "$\"+&[N!=8!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+b;0m )*!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+&>.VJ$!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+b;0m)*!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+IX] \"R(!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+DrauC!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+IX]\"R(!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+x dDSb!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+`([7&=!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+xdDSb!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+lH x`T!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+7G['Q\"!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+lHx`T!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAIL G%*protectedG" }}{PARA 9 "" 1 "" {TEXT 208 48 "<-- exit quasiNewton (n ow at top level) = FAIL\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "I%FAILG%*pr otectedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "quasiNewton(1,x ->sin(x)^4,x->4*sin(x)^3*cos(x),4.,0.000001,100,10);" }}{PARA 9 "" 1 " " {TEXT 208 169 "\{--> enter quasiNewton, args = 1, proc (x) options o perator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4 *sin(x)^3*cos(x) end proc, 4., 0.1e-5, 100, 10" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*DxSd&!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+DxSd:!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!*DxSd&!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"*AXOf'!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+ss&*!#6 " }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+;u@.m!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$!('>s&*!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#G!#9" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"+Gg>s&*!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"#G!#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"#G!#9" }}{PARA 9 "" 1 "" {TEXT 208 46 "<-- exit quasiNewton (now at top level) = 0.\}" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"!F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "a daptiveNewton:=proc(x0,f::procedure,fp::procedure,eps,feps,N)\n" } {MPLTEXT 1 0 35 "local x,xx,xxx,alpha,delta,q,n,m;\n" }{MPLTEXT 1 0 19 "x:=x0; alpha:=1.;\n" }{MPLTEXT 1 0 15 "for n to N do\n" }{MPLTEXT 1 0 34 " xx:=x-alpha*evalf(f(x)/fp(x));\n" }{MPLTEXT 1 0 38 " xxx:=x x-alpha*evalf(f(xx)/fp(xx));\n" }{MPLTEXT 1 0 23 " delta:=abs(xxx-xx) ;\n" }{MPLTEXT 1 0 23 " q:=(xxx-xx)/(xx-x);\n" }{MPLTEXT 1 0 29 " m: =alpha/(1-q); alpha:=m;\n" }{MPLTEXT 1 0 63 " if abs(f(xxx))F0F$>F3$\"\"\"\"\"!?(F6FF1,&F0F<*&F3F<-I&eval fGF)6#*&-F'6#F0F<-F+FI!\"\"FF2,&F1F<*&F3F<-FE6#*&-F'6#F1F<-F+FSFKF F4-I$absGF)6#,&F2FF5*&FYF<,&F1FF7*&F3F<,&F F3F7@$32-FW6#-F'6#F2F-2F4F,O6$F2F3>F0F2I%FAILGF)F%F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "adaptiveNewton(1.,x->sin(x)^4,x->4* sin(x)^3*cos(x),0.000001,100,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$ \"%9 " 0 "" {MPLTEXT 1 0 24 "de bug(adaptiveNewton);\n" }{MPLTEXT 1 0 68 "adaptiveNewton(1.,x->sin(x)^ 4,x->4*sin(x)^3*cos(x),0.000001,100,10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "I/adaptiveNewtonG6\"" }}{PARA 9 "" 1 "" {TEXT 208 169 "\{--> enter adaptiveNewton, args = 1., proc (x) options operator, arrow; sin(x)^4 end proc, proc (x) options operator, arrow; 4*sin(x)^3*cos(x) end pro c, 0.1e-5, 100, 10" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "$\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+(o![1h!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "$\"+L3xcV! 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