From fbd512828b9aa86781af6e5c95acd55c862e7baa Mon Sep 17 00:00:00 2001 From: qian <2152132@tongji.edu.cn> Date: Tue, 2 Jun 2026 01:01:49 +0800 Subject: [PATCH] fix: correct week12 Q3 convergence iteration count --- week12_full_materials/lecture12.pdf | Bin 930626 -> 581146 bytes week12_full_materials/lecture12.tex | 4 ++-- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/week12_full_materials/lecture12.pdf b/week12_full_materials/lecture12.pdf index a4102f04b03202de829ef8db3c0d9ad608cb3fb4..989f9a4121d30618cfa882a5046845712ee83f09 100644 GIT binary patch delta 552123 zcma&NQ*fZczqOkQCbn(c=ESy*iEX}dCbluLF|lpiwr!vPuJ2Txz3Wu%`tJI!tNWtY zv)1}`-w{_v2Pr_VC@N0R%)kyqesFX70>jEd#6)CoYz4!|$0%-T<6`E-C~jlqVkT;4 zVsC23C~IbC?qWg2%+10iAOPd+;$&uI3*)hNsXZP;+X}yVO#1<*E*hUtmb*I$k_fU2 zaiSL|#$P{1^4&cef2OBltAS|8gxb?`ExSW4Q zLjr@x2C3b^Yscp+qf3Dyo@c9XO!JN$3D91_KH&9!@qOD{cy&8H-EBm59md0fQ-|Xj z*SMusamjZ>H1COOhQCtS>r}!XPABe>NEO{^=Wkjq^*BW~K5mHInp-d=f#RbAIU4m& zP%&_-4_xj~5q~endf-@DCxnDjPu=PEXU|w1$A5{NCOk95cJRgw4f?~f3;!k`HX^`% zGJ$@&J(sU^P80z>)Kw?PbPPhML|cms)6v#`)z zhEZBqTK{voDWr!p4myRSM3v1SPw}jS2urS13^4Tk*3ZISVF8Cj_??0F{&-JoL!P)` zc?y@vcf7*Kq?OIjoI0-4${$E~&7J}Toca|i3O>qe{RGRjRM)A$*v z{(-}{FdB3T`Pijnqj$8iN=d4}i(>B|gUz;g02mrQ8F$_ex#K%4#E9bBoDLme4bY-oojd3z z_KT2RKRDJZPHNP{ZSz6wbY1dJ7VgSpX~G_VV_GAtQ1F{i{q3ta+l=L*4R{?TjcrWD zzOJt?$W4n;_*z7)w)ZGx#5@uDw#WIuFdz6=rzU*+~UMBYc$hFEHr+GjRkB9 z!U2YDrr3Hau}56!M3ps+FkH+Z`Y{g7kXqj;f7c+$9|H=hZceJ_P@gV=!N0bSk>Ggs zo`3KTgC6p(q*gnQ`ThFwqXP-$k!5e5;owdbI~2pAM+zVDDK+Vc_TTCInYnJZRX^co z{BCgm3#7})c^PbFLekqF6i|V;APA<;ok}9m^`jz)$6oVu>mN@`P%BU4RC^!>n%Nd} zEuUN~4qhFi~3BeuFzBzj-@?btu`tb)dA z4H*H&kYeZzZ3~)_ejWH0g@9Sb(r1GrW_v=0qvYYWh*D70nkErnM1WVcH*2w z=ogB%;{rhmepkUc=kVZc9BxzfKnO*_FzAt%YHs|gZsyuA(}!weRj;BWp(Mr39C6Vr z^T!4kfyRuy&kjG4Su2n;a^V->#^bVsA5)$pDpRP43!e-o?W>P3+!3Ws^QO`3>>Q*` zEAqIeJ`F}s8Jt@5$v^?U-nKSPvstpY5=H8s^;{rK>39ToKDUU(-A4xsPK_dZY5sq61@IO_uv*WhQ<<24jBdpHfI}#) z-1wr?6f5qN3+PgH7OkAN3K&X@+_JM-o>JxTr_YO}9_3;Z1pppKN7+@=O62K{+>D&Kg9(ZH1W*>;u>8Cx7rjEq14Po?~^~nwGjG7RA zmqH*wOrW2VoAEnzkPuN<07;+QXo~9(jj^O8m#4N;)A(%dV+^x!c6*i=^fn? z5tN(KCSePsE}*$DIMui&4lKgSwKlA1hmcvVJHed24;6h$1-fB)$9#31au#+&HW%D> zK{x+#W4Xn)yKQzzNB=7r{lZq)bcxQuOZV;e@&E2y_7GyHC?%Ua-@5sIGYG!MnqzR3 zq+hyu*7#-}nFiR#b-k_``)NFQ)naxo&hiw&0JoUh>geJZSMpUyDQfLy%#%%{dU?Ou zPb2LVv(`Jcg)!|ac-^-O8_fJ|!_Q!GMRwbY0~ZjZPe$igtbsA*!ujJ9r;=m&hXnchpf_+MD1dF*d! zbx}N2E)+4zi_7CCV zkPNmC)Ll|*KDWCy$NS#}yT8;JHw~b-;>@un7y}V_ccy-ju1n$zozYR+m)$RE>Hi!N zmo!}IpqHtgecyB0iHbJLmJiDbBYSbm z7BBfbH3(P+3j*}vf24x<5n1k7aEdOfUDEJQ??QV=E-Q4+ny3hU0IkhLM;bMfP_bZ=G$t7@vu;liauOaG5iK(^i zvst=SStFKLrXWYi(*sSeZucQ@SO$E2rrmXPR6yS^KPN>EqBr2a==j={sTgAOZlgAP z8Su$xnCB^c=8S67(M0@h)+0xqtMW-VIi3#z3;n<)BHdy^m?QUo8a91T?gC8#!K;TH z4J!;ilK8j!?fTf+HDWfdhaYq6`e%wDVH~Tcyim-d(33?6q685q`2rNqgT+tc*k90P zJ-`sN--N(H8?lbFUp-=zaZ|QuT0_1e0YW_z_W7nf82!8W6UA~El${G7TNReL!9r}D ztn@vO;O9##lR&O;^BQCEmrJGW@|Rn+SX$)|Y!<+2I{;%bpL;zuf7O{iqktW2*Z+6k zV{!@vR4x&A>OKlp#|-uj0-D%~To~>QC9pC&EMM4O%Q6iA*xTKWJZnXmV&J_I`fexJ z6?z~idHe4gv%n9@GaZeRpvdZ=h{&&N+jjJt)mp0*)> z7(WZ#n>}+JSY`OP6Lff$M$M-ZIMhTP-o!v#NWfM3&J#5lQYFv%c#XC%y(iXLpXrAX z7aUiiFqovH$rX4Dl&MHhCVYcwkt+p2L*dYmPF}|=f@Wuks3-Ogko43rr5tj)Wf8ikz^V!E%eKR zqS577w&qo}-2b{kka1mgB^Rl)z^YFx{}EmxY3Bq_aWWD^&%JAxBm54+4y-ch=azv? z>KjL-Q?lsbs0{Q#%qV(E$_?zF*sQN^Au}K^2{1MypzF$n%31GTeSuz@cLbuAW7|b80*S(ihl5m@TL&1A|c3YfeDD%|{ zSBKRW3%MhrDscI)*AC8_eJD(cBtiH>hncWV0ogCz8Z=^DAGy8qH~YUwYr0>|aRGlg zL0<)If3v&PP0G)dO=IPs`1A_)e`rU{D<2wCr2CTs=9D^CeX;9YENJAu91<;P{ z9W1P5yyX=!On)5Z;`xi`Tjtc@y3ouqx(V}2w>F^Vq*TLoe3wR0TA21#wuSG}Mf~AIprn zyTrJ}B)+a*n@qk7x*&KA&jeJ+pr3;~JD+E^`K>XxDCo0}F6|_8Qo3RV|Ay|195^s;-yb7i~ z!LLSHJV5aqLJrs#s6<7Ll|NOVU=?2f+%)aZ|Q2(KYNRhgM&%?b242^vcfq)ovyf`lLgSnP{G+T^J*eZeFH3-NzOgB^{#3ng?y2Nao=<=D7~D

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0.01$,即$0.99^k < 10^{-4}$,$k > \frac{\ln 10^4}{\ln(1/0.99)} \approx 916.42$,因此至少需要$917$次。 \textbf{4.} $\frac{1}{\sqrt{1-0.95^2}} = \frac{1}{\sqrt{0.0975}} = 3.2$。误差上界$\leq 3.2$。 \textbf{5.} $\frac{2}{0.01^2}(0.01 + 0.99 \times 0.01 \times 100) = 20000 \times 1.01 \approx 20200$。 -\end{document} \ No newline at end of file +\end{document}