{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 "" 0 1 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plo t" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 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 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "Math 304, 2007-09-12" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "x := Vector([0.9,1.3,1.9,2.1 ,2.6,3.0,3.9,4.4,4.7,5,6,7,8,9.2,10.5,11.3,11.6,12,12.6,13,13.3]):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "y := Vector([1.3,1.5,1.85, 2.1,2.6,2.7,2.4,2.15,2.05,2.1,2.25,2.3,2.25,1.95,1.4,0.9,0.7,0.6,0.5,0 .4,0.25]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "points := [se q([x[k],y[k]],k=1..21)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'pointsG 777$$\"\"*!\"\"$\"#8F)7$F*$\"#:F)7$$\"#>F)$\"$&=!\"#7$$\"#@F)F67$$\"#E F)F97$$\"#IF)$\"#FF)7$$\"#RF)$\"#CF)7$$\"#WF)$\"$:#F47$$\"#ZF)$\"$0#F4 7$\"\"&F67$\"\"'$\"$D#F47$\"\"($\"#BF)7$\"\")FS7$$\"##*F)$\"$&>F47$$\" $0\"F)$\"#9F)7$$\"$8\"F)F'7$$\"$;\"F)$FVF)7$\"#7$FRF)7$$\"$E\"F)$FPF)7 $F+$\"\"%F)7$$\"$L\"F)$\"#DF4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "plot(points);" }}{PARA 13 "" 1 "" {GLPLOT2D 459 179 179 {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coF(7$$\"3)*************f6Fco$\"3a**************pF*7$$ \"#7F?$\"3w**************fF*7$$\"3)*************f7Fco$\"3++++++++]F*7$ $\"#8F?$\"3A+++++++SF*7$$\"32++++++I8Fco$\"3++++++++DF*-%'COLOURG6&%$R GBG$\"#5!\"\"$F?F?Fiq-%+AXESLABELSG6$Q!6\"F]r-%%VIEWG6$%(DEFAULTGFbr" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "n := LinearAlgebra:-Dimensio n(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#@" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "If we use a sin gle polynomial p(x), it must have a degree 20" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Digits := 1 6:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A := Matrix(n,n):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "for j from 1 to n do\n fo r k from 1 to n do\n A[j,k] := x[j]^(k-1)\n end do\nend do:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "z := LinearAlgebra:-LinearS olve(A,y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p := 0.0:\nfo r k from 1 to n do\n p := p + z[k]*t^(k-1)\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "p;" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#,L$\"1!G(egJ4QG!#7\"\"\"*&$\"1WR^zO@X:!#6F'%\"tGF'!\"\"*&$\"1gSg6*)* =!QF+F')F,\"\"#F'F'*&$\"1IpueE?PcF+F')F,\"\"$F'F-*&$\"1)4Hrm3cm&F+F')F ,\"\"%F'F'*&$\"1`'>y3_E6%F+F')F,\"\"&F'F-*&$\"1^CuG?wTAF+F')F,\"\"'F'F '*&$\"15?O'*3\">T*F&F')F,\"\"(F'F-*&$\"1A`QXQn&4$F&F')F,\"\")F'F'*&$\" 1A\">m!)!#8F')F,\"\"*F'F-*&$\"1S!4*p7Jw;FTF')F,\"#5F'F'*&$\"1_Ll7q ,(y#!#9F')F,\"#6F'F-*&$\"1Ns=(*\\T0P!#:F')F,\"#7F'F'*&$\"1nM;3hOBR!#;F ')F,\"#8F'F-*&$\"1$zQHE5/G$!#F')F,\"#;F'F'*&$\"1zorcQk`Q!#@F')F,\"#F'F-*&$\"1k#>&)e`X 4\"!#EF')F,\"#?F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot (p,t=0.9..13.3);" }}{PARA 13 "" 1 "" {GLPLOT2D 458 308 308 {PLOTDATA 2 "6%-%'CURVESG6$7gx7$$\"\"*!\"\"$\"1a^*********H\"!#:7$$\"1NeRsRY%3*! #;$\"1\"RO)y*eq7\"F-7$$\"1q;zWz#*o\"*F1$\"1.^D3\"QMw*F17$$\"1+v=<>R`#* F1$\"1whj*H`3Y)F17$$\"1NLe*)e&yL*F1$\"1`3\\9LAYtF17$$\"1+]PMQy1&*F1$\" 1U,-JmX>cF17$$\"1qm;zZM+ NF17$$\"1nTNh&\\#=5F-$\"1IRH#**pLb$F17$$\"1]PfefpE5F-$\"1xuJ(e\")*oOF1 7$$\"1ML$eNU^.\"F-$\"1W@\\-K\"*RQF17$$\"1n;zWz#*o5F-$\"12x7G_f\\\\F17$ $\"1++vLNr-6F-$\"1v=O(\\****['F17$$\"1M$3F7*\\O6F-$\"1V7R,\\z1#)F17$$ \"1nmm6ZGq6F-$\"18_ru;VD**F17$$\"1](o>P\"o*>\"F-$\"1#='H4pGL6F-7$$\"1M 3FK!y!H7F-$\"15gnbI&4E\"F-7$$\"1n_F-$\"1k4E#Q?i(=F-7$$\"1+]7*QZ'o ?F-$\"1%Qb$3='p+#F-7$$\"1LL3b(H6?#F-$\"1Bs>>:`d@F-7$$\"1++Dny&RK#F-$\" 1js+Hd*eH#F-7$$\"1mmTzfyYCF-$\"1)3z<#4r?CF-7$$\"1LL3vt'Rd#F-$\"1SPBP`< GDF-7$$\"1++vq([6q#F-$\"1;lEMXi4EF-7$$\"1mmThV\"pw#F-$\"1FfhRY*4k#F-7$ $\"1LL3_*zE$GF-$\"1]EHX%))\\m#F-7$$\"1++vUbW)*GF-$\"1._9t3q\"o#F-7$$\" 1mmTL6@kHF-$\"1U')\\&*3L\"p#F-7$$\"1L$3KZ))p*HF-$\"1u%R'zmd$p#F-7$$\"1 +++8ewHIF-$\"1-[S'>&=%p#F-7$$\"1m;z_JaiIF-$\"1&)f?!46Kp#F-7$$\"1LLe#\\ ?`4$F-$\"15R!of:2p#F-7$$\"1mm;s^(3;$F-$\"1K&)e;!Q9o#F-7$$\"1++v^)HkA$F -$\"1WDD8\"opm#F-7$$\"1m;/V>HhLF-$\"17ab\\H$Ri#F-7$$\"1LLLMS:'\\$F-$\" 1o0M*)*>!#77$$ \"1NL3\"=t@5&F-$\".E(f./#)>F]^l7$$\"1NL$eVc8;&F-$\".'*fz3#o>F]^l7$$\"1 NLe!pR0A&F-$\".FV:Z!e>F]^l7$$\"1LLLXHsz_F-$\".P>)Q7_>F]^l7$$\"1:/wU]99 `F-$\".%3`'H3&>F]^l7$$\"1+v=Src[`F-$\".k^\">A^>F]^l7$$\"1!e9wB*)HQ&F-$ \".JZ(QP`>F]^l7$$\"1l;/N8TF]^l7$$\"1Ie*)HbD'[&F-$\".j gj^3(>F]^l7$$\"1***\\Zs*4bbF-$\".*o,=(=*>F]^l7$$\"1l;/!Gxpn&F-$\"-(*RV wY?!#67$$\"1LLLN[&))z&F-$\"-Z(fn57#Feal7$$\"1***\\Z#GHmgF-$\"-A4l+=BFe al7$$\"1++]H\\i$>'F-$\"-xgcc0CFeal7$$\"1***\\U.d4K'F-$\",qUwLZ#!#57$$ \"1Ie*3)eQ(Q'F-$\",=Riv\\#Fjbl7$$\"1l;aFZ\"QX'F-$\",X]iD^#Fjbl7$$\"1!e k3:Hq['F-$\",1zAk^#Fjbl7$$\"1+v=uNC?lF-$\",xY+x^#Fjbl7$$\"1:/^(*zX`lF- $\",az;k^#Fjbl7$$\"1LL$3Usme'F-$\",$\\!4D^#Fjbl7$$\"1N$epDx'3nF-$\",*G \"QiZ#Fjbl7$$\"1LL3$4#oIoF-$\",X&pc3CFjbl7$$\"1mm;*[zQ4(F-$\"+>a(f>#! \"*7$$\"1l;H^NdIsF-$\"+'>_F3#Fhel7$$\"1mmT8wEntF-$\"+vQp$*>Fhel7$$\"1+ ]([!RwEuF-$\"+jt9n>Fhel7$$\"1ILL'>gi[(F-$\"+AR%)\\>Fhel7$$\"1+D1U$3g^( F-$\"+Fy#[%>Fhel7$$\"1l;z([cda(F-$\"+L$oC%>Fhel7$$\"1I3_LY]vvF-$\"+zq3 V>Fhel7$$\"1***\\#zFD0wF-$\"+Pn:Y>Fhel7$$\"1I$3(G!oPt(F-$\"+fls\"*>Fhe l7$$\"1mm;yKGiyF-$\"+n7d'3#Fhel7$$\"1IL31@0&*zF-$\"*p5`A#!\")7$$\"1*** **R$4#y7)F-$\"*KWxQ#F`il7$$\"1++vH$4xD)F-$\"*$HXXDF`il7$$\"1****\\Dxf( Q)F-$\"*S*=xEF`il7$$\"1+DJwXV]%)F-$\"*:%[CFF`il7$$\"1+]7F9F8&)F-$\"*7 \\sv#F`il7$$\"1]7`_)*oW&)F-$\"*:^xw#F`il7$$\"1+v$zF3hd)F-$\"*?lRx#F`il 7$$\"1]PM.n_2')F-$\"*:'zvFF`il7$$\"1***\\(G^%*Q')F-$\"*h\\Jx#F`il7$$\" 1+]iZV[y()F-$\"*`')Gq#F`il7$$\"1****\\mN-=*)F-$\")h_QD!\"(7$$\"1lm\"4w 0M/*F-$\")VH@BFh\\m7$$\"1KLLbzyo\"*F-$\")M]d?Fh\\m7$$\"1++v#3CdB*F-$\" )`f0>Fh\\m7$$\"1lm;5-m-$*F-$\")=S_5Fg\\l$\"($zD6 Fdam7$$\"1m;pP/WK5Fg\\l$\"(FWE\"Fdam7$$\"1+]ddU[X5Fg\\l$\"())pQ\"Fdam7 $$\"1$eRmhg=0\"Fg\\l$\"(@yU\"Fdam7$$\"1mTqvpBe5Fg\\l$\"(C>Y\"Fdam7$$\" 1ekBb^Uh5Fg\\l$\"(?[Y\"Fdam7$$\"1](oZL8Y1\"Fg\\l$\"(1NZ\"Fdam7$$\"1U5I 9:!y1\"Fg\\l$\"(I9Z\"Fdam7$$\"1LL$Qp*)42\"Fg\\l$\"(OoY\"Fdam7$$\"1mT&y gSV3\"Fg\\l$\"('3'R\"Fdam7$$\"1+](=_\"p(4\"Fg\\l$\"(>#[7Fdam7$$\"1M3() Q+b56Fg\\l$\"(OV4\"Fdam7$$\"1nm'eb3M7\"Fg\\l$\"&T:*!\"&7$$\"1n;pY#el8 \"Fg\\l$\"&!)y(Ffem7$$\"1nm^Pzq\\6Fg\\l$\"&w,(Ffem7$$\"1'*)4\"Q!Q8:\"F g\\l$\"&r)pFfem7$$\"1EJqQ\"oH:\"Fg\\l$\"&g*pFfem7$$\"1bjHR#)fa6Fg\\l$ \"&*4oFfem7$$\"1%e*))R$Gi:\"Fg\\l$\"&!RnFfem7$$\"1Ug2T&)[f6Fg\\l$\"&xr 'Ffem7$$\"1+DEU([F;\"Fg\\l$\"&m\"oFfem7$$\"19\"fDzjN;\"Fg\\l$\"&w#oFfe m7$$\"1Hd&G%)yV;\"Fg\\l$\"&D!oFfem7$$\"1WB:$*Q>l6Fg\\l$\"&_k'Ffem7$$\" 1e*[M%*3g;\"Fg\\l$\"&ri'Ffem7$$\"1(=US/Rw;\"Fg\\l$\"&@t'Ffem7$$\"1;ajW \"p#p6Fg\\l$\"&?z'Ffem7$$\"1I?$\\>%3q6Fg\\l$\"&Tr'Ffem7$$\"1X'G_C**3< \"Fg\\l$\"&R)oFfem7$$\"1g__&H9<<\"Fg\\l$\"&#HqFfem7$$\"1u=#eMHD<\"Fg\\ l$\"&`e'Ffem7$$\"1*[=hRWL<\"Fg\\l$\"&4y'Ffem7$$\"1/^TY%fT<\"Fg\\l$\"&< 'oFfem7$$\"1=6y\"=\"Fg\\l$\"&5t'Ffem7$$\"1mT?#psx=\"Fg\\l$\"&`>+>\"Fg\\l$\"&Xq'Ffem7$$\"1CJ]y%o2>\"Fg\\l$\"&(pkFfem7$$\"1ky2Du^ \">\"Fg\\l$\"&[h'Ffem7$$\"1/ElrjE#>\"Fg\\l$\"&$3nFfem7$$\"1WtA=`,$>\"F g\\l$\"&:o'Ffem7$$\"1$3-[EkP>\"Fg\\l$\"&>u'Ffem7$$\"1AoP6K^%>\"Fg\\l$ \"&4V'Ffem7$$\"1i:&z:i_>\"Fg\\l$\"&-'oFfem7$$\"1-j_/6,'>\"Fg\\l$\"&_\\ 'Ffem7$$\"1U55^+w'>\"Fg\\l$\"&hS'Ffem7$$\"1@0DWzD)>\"Fg\\l$\"&\"Fg\\l$\"&iK'Ffem7$$\"1m;4u)*[87Fg\\l$\"&Ai&Ffem7$$\"1LL y5RAF7Fg\\l$\"&Zt$Ffem7$$\"1mT&Q&eOL7Fg\\l$\"&LQ$Ffem7$$\"1+]#pz2&R7Fg \\l$\"&>4$Ffem7$$\"1Me**R(\\cC\"Fg\\l$\"&(3LFfem7$$\"1nm1$o\"z^7Fg\\l$ \"&Fs$Ffem7$$\"1M3xn)))[E\"Fg\\l$\"%6G\"Fg\\l$\"%f%*Fhcn7$$ \"1iS^^M!>G\"Fg\\l$\"%<$*Fhcn7$$\"1v=KJpo#G\"Fg\\l$\"%u'*Fhcn7$$\"1)oH 6TqMG\"Fg\\l$\"%%\\*Fhcn7$$\"1+v$4*QD%G\"Fg\\l$\"%o&*Fhcn7$$\"1](o,\"y Q(G\"Fg\\l$\"%_))Fhcn7$$\"1++SH<_!H\"Fg\\l$\"%C%)Fhcn7$$\"1]7j[cl$H\"F g\\l$\"%XwFhcn7$$\"1+D'yc*y'H\"Fg\\l$\"%jaFhcn7$$\"17.nZId(H\"Fg\\l$\" %mfFhcn7$$\"1D\"yu_c$)H\"Fg\\l$\"%gfFhcn7$$\"1QfG2+9*H\"Fg\\l$\"%MaFhc n7$$\"1]P4([B**H\"Fg\\l$\"%\\XFhcn7$$\"1v$4nW!\\,8Fg\\l$\"%@BFhcn7$$\" 1+]K1u0.8Fg\\l$\"$b*Fhcn7$$\"1)oH%=8u/8Fg\\l$!$\\(Fhcn7$$\"1vV`I_U18Fg \\l$!%x>Fhcn7$$\"1i!RE94\"38Fg\\l$!%WOFhcn7$$\"1]PuaIz48Fg\\l$!%$p%Fhc n7$$\"1%4'z5]j58Fg\\l$!%&=(Fhcn7$$\"1Q%[o'pZ68Fg\\l$!%P\")Fhcn7$$\"1#y +H#*=BJ\"Fg\\l$!%AtFhcn7$$\"1DJ&*y3;88Fg\\l$!%5&*Fhcn7$$\"17y0\"zW[J\" Fg\\l$!&L/\"Fhcn7$$\"1+D;.(GlJ\"Fg\\l$!&@A\"Fhcn7$$\"1)=n_h7#=8Fg\\l$! &HF\"Fhcn7$$\"1v=PFl*)>8Fg\\l$!&>H\"Fhcn7$$\"1=UU$[Q2K\"Fg\\l$!&*f8Fhc n7$$\"1ilZR/e@8Fg\\l$!&#)H\"Fhcn7$$\"11*GbRACK\"Fg\\l$!&WM\"Fhcn7$$\"1 ]7e^VEB8Fg\\l$!&'=7Fhcn7$$\"1%fLwI1TK\"Fg\\l$!&FD\"Fhcn7$$\"1Qfoj#[\\K \"Fg\\l$!&>9\"Fhcn7$$\"1#GQ(>-zD8Fg\\l$!%i!*Fhcn7$$\"1D1zv@jE8Fg\\l$!% >()Fhcn7$$\"1oH%=8uuK\"Fg\\l$!%!R(Fhcn7$$\"17`*y3;$G8Fg\\l$!%lFFhcn7$$ \"1cw%R/e\"H8Fg\\l$!$*)*Fhcn7$$\"$L\"F*$\"%.HFhcn-%'COLOURG6&%$RGBG$\" #5F*$\"\"!F]aoF\\ao-%+AXESLABELSG6$Q\"t6\"Q!Fbao-%%VIEWG6$;F(Fb`o%(DEF AULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve \+ 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "In applications, we rarely use a polynomial of degree 10 or mor e." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "14 1 0" 65 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }