《数值分析》习题答案

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1、д乬11ˊҹϟ৘㸼⼎ⱘ䖥Ԑ᭄ˈ䯂݋᳝޴ԡ᳝ᬜ᭄ᄫ˛ᑊᇚᅗ㟡ܹ៤᳝ᬜ᭄DŽ*˄1˅˙x451.023ˈ˙x451.01˗11*˄2˅˙xˉ0.045113ˈ˙xˉ0.04518˗22*˄3˅˙x23.4213ˈx˙23.4604˗33*1˄4˅˙xˈx˙0.3333˗443*˄5˅˙x23.496ˈ˙x23.494˗55*55˄6˅˙x96Üˈ10x˙96.1Ü˗1066*3˄7˅˙x0.00096ˈx˙0.96Ü10˗77*˄8˅˙xˉ8700ˈx˙ˉ8700.3DŽ88*㾷˖(1)x451.023x451.0111*

2、11xx0.01310ˈ݋x᳝4ԡ᳝ᬜ᭄ᄫDŽx451.011112*(2)x0.045113x0.045182214*1310xx0.045180.045113=0.000067102222x2݋᳝2ԡ᳝ᬜ᭄ᄫˈx20.045*(3)x23.4213x23.460433*11xx23.421323.460423.460423.42130.039110332x݋᳝3ԡ᳝ᬜ᭄ᄫˈx23.4(ϡ㛑ݭЎ23.5)33*1(4)xˈx0.3333443*14x

3、4x40.00003310,x4݋᳝4ԡ᳝ᬜ᭄ᄫˈx40.33332*(5)x523.496ˈx523.494*12x5x523.49623.4940.002102x5݋᳝4ԡ᳝ᬜ᭄ᄫˈx523.50(ϡ㛑ݭЎ23.49)*5757(6)x696100.9610x696.1100.96110*7127x6x60.001101010275x6݋᳝2ԡ᳝ᬜ᭄ᄫˈx60.96109610*3(7)x70.00096x70.9610*3*x70

4、.9610x7x70x7㊒⹂*(8)x88700x88700.3*10x8x80.310x8݋᳝4ԡ᳝ᬜ᭄ᄫˈx88700㊒⹂22.ҹϟ৘᭄ഛЎ᳝ᬜ᭄ᄫ˖(1)0.1062+0.947;(2)23.46̣12.753;(3)2.7476.83;(4)1.473/0.064DŽ䯂㒣䖛Ϟ䗄䖤ㅫৢˈޚ⹂㒧ᵰ᠔೼ⱘ᳔ᇣऎ䯈ߚ߿ᰃҔМ˛㾷˖(1)x1=0.1062ˈx2=0.947ˈx1+x2=1.05321413e(x1)10ˈe(x2)10221413e(x1x2)e(x1)e(x2)

5、e(x1)e(x2)101022=0.00055**x1x2[1.05320.00055ˈ1.0532+0.00055]=[1.05265ˈ1.05375](2)x1=23.46ˈx212.753x1x210.7071213e(x1)10ˈe(x2)1022e(x1x2)e(x1)e(x2)e(x1)e(x2)12131010=0.005522**x1x2[10.7070.0055,10.707+0.0055]=[10.7015,10.7125](3)x12.747x2

6、6.83x1x218.76201,1312e(x1)10,e(x2)1022e(x1x2)x2e(x1)x1e(x2)x2e(x1)x1e(x2)1312126.83102.7471010(0.683+2.747)=0.01715222**x1x2[18.762010.01715,18.762010.01715][18.74486,18.77916](4)x11.473,x20.064,x1x223.015625e(x)1103,e(x)1103e(x1)1e

7、(x)x1e(x)1212222x2x2x2e(x1)1e(x)x1e(x)111031.47311031222x2x2x20.06420.0642=0.187622*x1[23.0156250.187622,23.015625+0.187622]*x2=[22.828003,23.203247]23.ᇍϔܗ2⃵ᮍ⿟x40x10ˈབᵰ39919.975݋᳝5ԡ᳝ᬜ᭄ᄫˈ∖݊݋᳝5ԡ᳝ᬜ᭄ᄫⱘḍDŽ2㾷˖x40x102x40x400399**1x120399,x22039920399*

8、13䆄x399,x19.975e(x)10213x120x=20+19.975=39.975e(x1)e(x2)102x1݋᳝5ԡ᳝ᬜ᭄ᄫDŽ111x20.025015634720x2019.97539.975e(x)e(x2)ˈ2(20x)1310e(x)2616e(x)0