{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 0 0 0 0 2 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 } {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 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 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 3 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 Outpu t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 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 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "Prevzorkovani" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Asuume some f unction, for instance:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "f :=x->subs(x=x/7,sin(x)+cos(3*x)+x*sin(5*x)+ln(x)*sin(cos(x))-ln(x+2)*c os(sin(x))-x*(cos(6*x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6 #%\"xG6\"6$%)operatorG%&arrowGF(-%%subsG6$/9$,$F0#\"\"\"\"\"(,.-%$sinG 6#F0F3-%$cosG6#,$F0\"\"$F3*&F0F3-F76#,$F0\"\"&F3F3*&-%#lnGF8F3-F76#-F: F8F3F3*&-FE6#,&F0F3\"\"#F3F3-F:6#F6F3!\"\"*&F0F3-F:6#,$F0\"\"'F3FPF(F( F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=x->ln(x)+sin(x)-x* sin(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)opera torG%&arrowGF(,(-%#lnG6#9$\"\"\"-%$sinGF/F1*&F0F1F2F1!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" 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l7$$\"3[i:&G]T(GFh_l7$$\"31e9TsptLR \"=i\">Fh_l7$$\"3+a8(>WK(QFh_l7$$\"3$*\\7`6zsVFh_l7$$\"3#=/^1&)=Pv\"Fh_l$\"3Wr4Z]cB&)=Fh_l7$$\"3ML3x* y4Pw\"Fh_l$\"3_;PO+H.X=Fh_l7$$\"3)oTN11r?y\"Fh_l$\"36wlpvI2Hh:Fh_l7$$\"3lm\"z*>kZ@=Fh_l$\"3BL,'[nv5J\"Fh _l7$$\"3CL$e%30_U=Fh_l$\"3G!e&4v'=)35Fh_l7$$\"3!)*\\i?fU8'=Fh_l$\"3D1( QJL*RWqF^r7$$\"3qmmmvY;!)=Fh_l$\"3Kfcml-['y$F^r7$$\"3)[P4\"4))>!*=Fh_l $\"3xC)pn/d5+#F^r7$$\"3T$3_D%HB+>Fh_l$\"3IT^9jho\\?Fgr7$$\"3&>z%*f2n- \">Fh_l$!3!fr)z5kX$e\"F^r7$$\"39+vV47I?>Fh_l$!31QR!)=pwXLF^r7$$\"3&)** **\\,\"4&R>Fh_l$!3u87!opV(zlF^r7$$\"3#**\\iN*pre>Fh_l$!37S_ueMWD&*F^r7 $$\"3'*\\7y'\\e$z>Fh_l$!3Fi1\"e%*3OA\"Fh_l7$Fcq$!3`$4F!\\F-N9Fh_l-%'CO LOURG6&%$RGBG$FW!\"\"F*F*-%+AXESLABELSG6$Q\"w6\"Q!Fhdm-%%VIEWG6$;F'Fcq %(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "C urve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "K:=2.3;NN:=20/K;\nz:=seq(i*K ,i=1..NN);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG$\"#B!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#NNG$\"+u@l&p)!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG6*$\"#B!\"\"$\"#YF($\"#pF($\"##*F($\"$:\"F($\" $Q\"F($\"$h\"F($\"$%=F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "We von t to recompute 20 values into 16 values using the aproximation of the \+ values:" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Methodes" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1388 "Spl2:=proc(x,y)# kubicky splain\nlocal N,K,j,a,b,c, Q,z;\nN:=nops(x); # pocet bodu\nK:=N-2; # pocet polynomu\na := -(x[3]* y[1]-x[1]*y[3]-y[1]*x[2]+x[2]*y[3]-x[3]*y[2]+x[1]*y[2])/(-x[2]*x[3]^2+ x[1]^2*x[2]+x[1]*x[3]^2+x[3]*x[2]^2-x[3]*x[1]^2-x[1]*x[2]^2); \nb := ( -x[1]^2*y[3]+x[1]^2*y[2]+x[2]^2*y[3]+y[1]*x[3]^2-y[1]*x[2]^2-y[2]*x[3] ^2)/(-x[2]*x[3]^2+x[1]^2*x[2]+x[1]*x[3]^2+x[3]*x[2]^2-x[3]*x[1]^2-x[1] *x[2]^2); \nc := (x[1]^2*x[2]*y[3]-x[1]^2*x[3]*y[2]-x[2]^2*x[1]*y[3]+y [2]*x[1]*x[3]^2-y[1]*x[2]*x[3]^2+x[2]^2*x[3]*y[1])/(-x[2]*x[3]^2+x[1]^ 2*x[2]+x[1]*x[3]^2+x[3]*x[2]^2-x[3]*x[1]^2-x[1]*x[2]^2);\np[1]:=a*z^2+ b*z+c;\n# Pvni (kubicky) polynom vztvorim tak, ze bude prochazet prvni mi trema body\n\nQ:=z%%Spl2Gf*6$%\"xG%\"yG6-%\"NG%\"KG%\"jG%\"aG%\"bG% \"cG%\"QG%\"zG%\"pG%\"iG%$derG6\"F5C,>8$-%%nopsG6#9$>8%,&F8\"\"\"\"\"# !\"\">8',$*&,.*&&F<6#\"\"$F@&9%6#F@F@F@*&&F8(*& ,.*&FgnF@FQF@FB*&FgnF@FWF@F@*&FjnF@FQF@F@*&FLF@FenF@F@*&FLF@FjnF@FB*&F WF@FenF@FBF@FYFB>8)*&,.*(FgnF@FSF@FQF@F@*(FgnF@FIF@FWF@FB*(FjnF@FPF@FQ F@FB*(FWF@FPF@FenF@F@*(FLF@FSF@FenF@FB*(FjnF@FIF@FLF@F@F@FYFB>&8,FN,(* &FDF@)8+FAF@F@*&F^oF@FgpF@F@FhoF@>8*6$2FgpFIFbp?(8-FAF@F>%%trueGC)>8&, &F^qF@F@F@>8.,&*&FDF@&F<6#FbqF@FAF^oF@>F^o,$*&,**&FhqF@&FMFiqF@!\"#*(F AF@FhqF@&FM6#,&FbqF@F@F@F@F@*&)FhqFAF@FeqF@F@*&FeqF@)&FFD*&,*F_rFB*&FirF@FeqF@FBFbrF@ *&FhqF@FeqF@F@F@FjrFB>Fho*&,,*(FfrF@FirF@FeqF@F@*&FfrF@FbrF@F@*(FhqF@F eqF@FhrF@FB*&F_rF@FhrF@F@**FAF@F_rF@FirF@FhqF@FBF@FjrFB>&Fcp6#F^qFdp@% 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