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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 93 "Egy p\351lda arra, hogy \+
f\374ggv\351nyek illeszt\351se polinommal kellemetlen meglepet\351sekh
ez vezethet..." }}{PARA 256 "" 0 "" {TEXT -1 35 "A Csebisev-sorfejt
\351s biztons\341gosabb" }}{PARA 257 "" 0 "" {TEXT -1 34 "Bartha Feren
c, SZTE, 2003. febru\341r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
61 "restart:with(CurveFitting):with(numapprox):with(orthopoly,T):" }}}
{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 32 "Legyen az illesztend\365 f
\374ggv\351ny: " }{XPPEDIT 19 1 "f:=1/(1+25*x^2):" "6#>%\"fG*&\"\"\"F&
,&F&F&*&\"#DF&*$%\"xG\"\"#F&F&!\"\"" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
38 "plot(f,x=-1..1,axes=box,title=`f(x)`);" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 63 "Most tabul\341ljuk 21 ekvidiszt\341ns pontban a [-1,
1] intervallumon:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dx:=1/10:lis:=
seq([k*dx,subs(x=k*dx,f)],k=-10..10):" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 91 "A MAPLE bels\365 rutinj\341t haszn\341ljuk, hogy egy
 interpol\341l\363 polinomot k\351sz\355ts\374nk a t\341bl\341zathoz:
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "P:=PolynomialInterpolation([lis
],x):print('P(x)'=P);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 60 "Per
sze a k\351plet nem t\372l besz\351des, n\351zz\374k ink\341bb a grafi
kont:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 
50 "plot([P,f],x=-1..1,axes=box,title=`P(x) \351s f(x)`);" }}{PARA 0 "
" 0 "" {MPLTEXT 0 21 44 "Figyelj\374nk a f\374gg\365leges tengely beos
zt\341s\341ra!" }}{PARA 0 "" 0 "" {MPLTEXT 0 21 24 "A kapott g\366rbe \+
aggaszt\363!" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 48 "Most a MAPLE
 Csebisev-sort illeszt a f\374ggv\351nyre:" }{TEXT -1 0 "" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 45 "C:=chebyshev(f,x=-1..1,0.03):print('C(x)'=C)
;" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 56 "Az \355gy kapott (ugyan
olyan foksz\341m\372) polinom m\341r eg\351sz j\363" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 50 "plot([C,f],x=-1..1,axes=box,title=`C(x) \+
\351s f(x)`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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