数值分析报告上机题(matlab版)(东南大学)Word下载.doc
《数值分析报告上机题(matlab版)(东南大学)Word下载.doc》由会员分享,可在线阅读,更多相关《数值分析报告上机题(matlab版)(东南大学)Word下载.doc(23页珍藏版)》请在冰点文库上搜索。
![数值分析报告上机题(matlab版)(东南大学)Word下载.doc](https://file1.bingdoc.com/fileroot1/2023-4/28/b0576dd3-aca6-494e-971a-405ce8c96048/b0576dd3-aca6-494e-971a-405ce8c960481.gif)
,Sn1);
Caculatefromsmalltolarge%f\n'
Sn2);
三、求解结果
10^2
ThevalueofSnusingdifferentalgorithms(N=100)
____________________________________________________
AccurateCalculation0.740049
Caculatefromlargetosmall0.740049
Caculatefromsmalltolarge0.740050
10^4
ThevalueofSnusingdifferentalgorithms(N=10000)
AccurateCalculation0.749900
Caculatefromlargetosmall0.749852
Caculatefromsmalltolarge0.749900
10^6
ThevalueofSnusingdifferentalgorithms(N=1000000)
AccurateCalculation0.749999
Caculatefromsmalltolarge0.749999
四、结果分析
有效位数
n
顺序
100
10000
1000000
从大到小
6
3
从小到大
5
可以得出,算法对误差的传播又一定的影响,在计算时选一种好的算法可以使结果更为精确。
从以上的结果可以看到从大到小的顺序导致大数吃小数的现象,容易产生较大的误差,求和运算从小数到大数算所得到的结果才比较准确。
第二章
(1)给定初值及容许误差,编制牛顿法解方程f(x)=0的通用程序。
(2)给定方程,易知其有三个根
a)由牛顿方法的局部收敛性可知存在当时,Newton迭代序列收敛于根x2*。
试确定尽可能大的。
b)试取若干初始值,观察当时Newton序列的收敛性以及收敛于哪一个根。
(3)通过本上机题,你明白了什么?
文件search.m
%%寻找最大的delta值%%
%%
flag=1;
k=1;
x0=0;
whileflag==1
delta=k*10^-6;
x0=delta;
k=k+1;
m=0;
flag1=1;
whileflag1==1&
&
m<
=10^3
x1=x0-fx(x0)/dfx(x0);
ifabs(x1-x0)<
10^-6flag1=0;
end
m=m+1;
x0=x1;
end
ifflag1==1||abs(x0)>
=10^-6flag=0;
end
Themaximundeltais%f\n'
delta);
文件fx.m
%%定义函数f(x)
functionFx=fx(x)
Fx=x^3/3-x;
文件dfx.m
%%定义导函数df(x)
functionFx=dfx(x)
Fx=x^2-1;
文件Newton.m
%%Newton法求方程的根%%
ef=10^-6;
%给定容许误差10^-6
k=0;
x0=input('
PleaseinputinitialvalueXo:
kXk'
0%f\n'
x0);
whileflag==1&
k<
ef
flag=0;
%d%f\n'
k,x0);
end
1.运行search.m文件
结果为:
Themaximumdeltais0.774597
即得最大的δ为0.774597,Newton迭代序列收敛于根=0的最大区间为(-0.774597,0.774597)。
2.运行Newton.m文件
在区间上各输入若干个数,计算结果如下:
区间上取-1000,-100,-50,-30,-10,-8,-7,-5,-3,-1.5
13-1.732051
-30
kXk
0-30.000000
1-20.022247
2-13.381544
3-8.971129
4-6.056000
5-4.150503
6-2.937524
7-2.215046
8-1.854714
9-1.743236
10-1.732158
11-1.732051
12-1.732051
-10
0-10.000000
1-6.734007
2-4.590570
3-3.212840
4-2.371653
5-1.922981
6-1.757175
7-1.732580
8-1.732051
9-1.732051
-10000
0-10000.000000
1-6666.666733
2-4444.444589
3-2962.963209
4-1975.309031
5-1316.873025
6-877.915856
7-585.277997
8-390.186470
9-260.126022
10-173.419911
11-115.617118
12-77.083845
13-51.397880
14-34.278229
15-22.871618
16-15.276949
17-10.228459
18-6.884780
19-4.688772
20-3.274807
21-2.407714
22-1.939750
23-1.761259
24-1.732762
25-1.732051
26-1.732051
-100
0-100.000000
1-66.673334
2-44.458891
3-29.654263
4-19.792016
5-13.228447
6-8.869651
7-5.989231
8-4.107324
9-2.910755
10-2.200189
11-1.848687
12-1.742235
13-1.732139
14-1.732051
15-1.732051
-50
0-50.000000
1-33.346672
2-22.251125
3-14.864105
4-9.954458
5-6.703960
6-4.571013
7-3.200520
8-2.364515
9-1.919703
10-1.756405
11-1.732548
-3
0-3.000000
1-2.250000
2-1.869231
3-1.745810
4-1.732212
5-1.732051
6-1.732051
-1.5
0-1.500000
1-1.800000
2-1.735714
3-1.732062
4-1.732051
-8
0-8.000000
1-5.417989
2-3.739379
3-2.684934
4-2.078246
5-1.802928
6-1.736023
7-1.732064
-7
0-7.000000
1-4.763889
2-3.322318
3-2.435533
4-1.952915
5-1.764630
6-1.732931
7-1.732051
-5
0-5.000000
1-3.472222
2-2.524180
3-1.996068
4-1.776618
5-1.733674
6-1.732053
结果显示,以上初值迭代序列均收敛于-1.732051,即根。
在区间即区间(-1,-0.774597)上取-0.774598,-0.8,-0.85,-0.9,-0.99,计算结果如下:
-0.774598
0-0.774598
10.774605
2-0.774645
30.774884
4-0.776324
50.785049
6-0.840641
71.350187
81.993830
91.775963
101.733628
111.732053
121.732051
131.732051
-0.8
0-0.800000
10.948148
2-5.625370
3-3.872625
4-2.766197
5-2.121367
6-1.818292
7-1.737822
8-1.732079
10-1.732051
0.85
00.850000
1-1.475375
2-1.819444
3-1.737969
4-1.732081
-0.9
0-0.900000
12.557895
22.012915
31.781662
41.734049
51.732054
61.732051
71.732051
-0.99
0-0.990000
132.505829
221.691081
314.491521
49.707238
56.540906
64.464966
73.133840
82.326075
91.902303
101.752478
111.732403
计算结果显示,迭代序列局部收敛于-1.732051,即根,局部收敛于1.730251,即根。
在区间即区间(-0.774597,0.774597)上,由search.m的运行过程表明,在整个区间上均收敛于0,即根。
0.774598
00.774598
1-0.774605
20.774645
3-0.774884
40.776324
5-0.785049
60.840641
7-1.350187
8-1.993830
9-1.775963
10-1.733628
11-1.732053
0.8
00.800000
1-0.948148
25.625370
33.872625
42.766197
52.121367
61.818292
71.737822
81.732079
91.732051
101.732051
0.9
00.900000
1-2.557895
2-2.012915
3-1.781662
4-1.734049
5-1.732054
0.99
00.990000
1-32.505829
2-21.691081
3-14.491521
4-9.707238
5-6.540906
6-4.464966
7-3.133840
8-2.326075
9-1.902303
10-1.752478
11-1.732403
12