问答题
多项式求根是一个病态问题，考虑多项式
p(x)=(x-1)(x-2)…(x-10)=a0+a1x+…+a9x9+x10求解扰动方程p(x)+εx9=0．
(1)产生系数a0，a1，…，a9.
(2)取ε=10-6，10-10用MATLAB求根函数计算扰动方程的根．分析ε对根的影响．
【正确答案】C=[1 2 3 4 5 6 7 8 9 10];
P=poly(C) ;
for i=1:11
a(i)=P(11-i+1) ;
end
a
e=[0 1e-6 0 0 0 0 0 0 0 0 0];
P1=P+e;
jie1=roots(P1)
e=[0 1e-8 0 0 0 0 0 0 0 0 01;
P1=P+e;
jie2=roots(P1)
e=[0 1e-10 0 0 0 0 0 0 0 0 0];
P1=P+e;
jie3=roots(P1)
a=
Columns 1 through 6
3628800 -10628640 12753576 -8409500 3416930 -902055
Columns 7 through 11
157773 -18150 1320 -55 1
jie1=
9.997229485963077
9.009544086090051
7.986687353782443
7.009401159520948
5.996516555488711
5.000679089922876
3.999939329265204
3.000001952659989
1.999999987303959
1.000000000002732
jie2=
9.999972441469870
9.000096078724452
7.999866849927122
7.000093415324802
5.999965010304080
5.000006781698407
3.999999393134254
3.000000019545915
1.999999999871073
1.000000000000068
jie3=
9.999999724624050
9.000000959779166
7.999998670863575
7.000000931354902
5.999999651892960
5.000000067129188
3.999999994077153
3.000000000179377
1.999999999999580
0.999999999999981
【答案解析】