实验报告文档格式.docx
- 文档编号:17268058
- 上传时间:2022-11-30
- 格式:DOCX
- 页数:28
- 大小:204.15KB
实验报告文档格式.docx
《实验报告文档格式.docx》由会员分享,可在线阅读,更多相关《实验报告文档格式.docx(28页珍藏版)》请在冰豆网上搜索。
end
s
(b)程序:
s=s+(5^n)/m;
s=s^(-1)
第三题:
formatlong
x=zeros(1,n);
x
(1)=1;
forn=2:
40
x(n)=x(n-1)*(1/3);
x
y=zeros(1,n);
y
(1)=1;
y
(2)=1/3;
forn=3:
y(n)=y(n-1)*(5/3)-y(n-2)*(4/9);
y
第四题:
syms('
x'
p=1;
forn=1:
20
k=x-n;
p=p*k;
p
p=
(x-1)*(x-2)*(x-3)*(x-4)*(x-5)*(x-6)*(x-7)*(x-8)*(x-9)*(x-10)*(x-11)*(x-12)*(x-13)*(x-14)*(x-15)*(x-16)*(x-17)*(x-18)*(x-19)*(x-20)
a=0.001;
solve(p+a*x^19)
实验结果与分析:
结果:
x=1
f
=
0.4142
g
2.4142
x=10^5
158.1135
632.4571
x=10^10
5.0000e+004
2.0000e+005
分析:
g(x)得到的值误差比较小,f(x)得到的值不够精确。
(a)结果:
s
-1.8271
e^(-5)=
(b)结果:
s=0.0070
(a)程序得到的值是错误的不可能得到负值,(b)程序得到的值才是正确的且比较精确。
x=
Columns1through5
1.000000000000000.333333333333330.111111111111110.037037037037040.01234567901235
Columns6through10
0.004115226337450.001371742112480.000457247370830.000152415790280.00005080526343
Columns11through15
0.000016935087810.000005645029270.000001881676420.000000627225470.00000020907516
Columns16through20
0.000000069691720.000000023230570.000000007743520.000000002581170.00000000086039
Columns21through25
0.000000000286800.000000000095600.000000000031870.000000000010620.00000000000354
Columns26through30
0.000000000001180.000000000000390.000000000000130.000000000000040.00000000000001
Columns31through35
0.000000000000000.000000000000000.000000000000000.000000000000000.00000000000000
Columns36through40
Columns41through45
00000
Columns46through50
0000
y=
0.000016935087810.000005645029270.000001881676420.000000627225480.00000020907516
0.000000069691720.000000023230580.000000007743530.000000002581180.00000000086040
0.000000000286810.000000000095620.000000000031900.000000000010660.00000000000360
0.000000000001250.000000000000490.000000000000260.000000000000220.00000000000025
0.000000000000320.000000000000420.000000000000560.000000000000740.00000000000099
0.000000000001320.000000000001760.000000000002350.000000000003130.00000000000417
(b)程序得到的值比(a)程序得到的值的有效数字位数多,而且比较准确。
ans=
1.0000000000000000000082206352466
1.9999999999999181103721686190831
3.0000000016338242385051980289015
3.9999978104089828369347555291761
5.0006096104478121611874253483110
5.9520830976335371098727215585573
6.7576088500695613373496582001525+.65470437943497632710244996169678*i
27.081684159350407690505468487979+5.0381247465156983767887546052646*i
7.6926762171569880425046987508124+1.8988377402395301624310643961314*i
8.9128216107583166664211102599600+3.4731727536571324572309009854627*i
19.533677749724924092104646513976+9.1664045168766385324548225474719*i
10.721140617251104725551635419601+5.4609012089932269126258921027995*i
13.823545535626660217122537507881+7.7716667287284791002538182683774*i
13.823545535626660217122537507881-7.7716667287284791002538182683774*i
10.721140617251104725551635419601-5.4609012089932269126258921027995*i
19.533677749724924092104646513976-9.1664045168766385324548225474719*i
8.9128216107583166664211102599600-3.4731727536571324572309009854627*i
7.6926762171569880425046987508124-1.8988377402395301624310643961314*i
27.081684159350407690505468487979-5.0381247465156983767887546052646*i
6.7576088500695613373496582001525-.65470437943497632710244996169678*i
a的值取的越小得到的结果越准确。
成绩:
教师签名:
月日
实验二:
各种插值多项式的程序。
熟练掌握各种插值多项式的做法及应用。
课本第二章课后上级习题。
牛顿插值多项式
X=[0.20.40.60.81.0];
Y=[0.980.920.810.640.38];
n=length(X);
A=zeros(n,n);
A(:
1)=Y'
;
forj=2:
n
fori=j:
A(i,j)=(A(i,j-1)-A(i-1,j-1))/(X(i)-X(i-j+1));
end
C=diag(A);
C=C'
P=C
(1)+C
(2)*(x-X
(1))+C(3)*(x-X
(1))*(x-X
(2))+C(4)*(x-X
(1))*(x-X
(2))*(x-X(3))+C(5)*(x-X
(1))*(x-X
(2))*(x-X(3))*(x-X(4))
p=sym2poly(P)
x=[0.2;
0.28;
1.0;
1.08]
y=polyval(p,x);
plot(x,y,'
--r.'
)
三次样条函数
m=length(X);
A=zeros(m,m);
n=m-1;
H=zeros(1,n);
lambda=zeros(1,n);
mu=zeros(1,n);
lambda
(1)=1;
A(1,1)=2;
A(1,2)=lambda
(1);
D=zeros(1,n);
H
(1)=X
(2)-X
(1);
mu
(1)=1;
D
(1)=3*(Y
(2)-Y
(1));
fork=1:
hk=X(k+1)-X(k);
H(k+1)=hk;
H=H(2:
n+1);
n-1
lambdak=H(k)/(H(k)+H(k+1));
lambda(k+1)=lambdak;
muk=1-lambda(k+1);
mu(k)=muk;
dk=3*((mu(k).*(Y(k+1)-Y(k))./H(k))+(lambda(k+1).*(Y(k+2)-Y(k+1))./H(k+1)));
D(k+1)=dk;
D(m)=3*(Y(m)-Y(m-1))/H(m-1);
mu(n)=1;
n;
H;
lambda;
mu;
D;
fori=1:
m-1
A(i,i)=2;
A(m,m)=2;
A(i,i+1)=lambda(i);
A(i+1,i)=mu(i);
dY=A\D'
symsx
S=zeros(m-1,1);
fork=2:
m
sk=Y(k-1)*((H(k-1)-2*X(k-1)+2*x)*(x-X(k))^2)/(H(k-1)^3)+Y(k)*((H(k-1)+2*X(k)-2*x)*(x-X(k-1))^2)/(H(k-1)^3)+dY(k-1)*((x-X(k-1))*(x-X(k))^2)/(H(k-1)^2)+dY(k)*((x-X(k))*(x-X(k-1))^2)/(H(k-1)^2)
p=sym2poly(sk)
多项式插值:
subplot(1,2,1);
fplot('
1/(1+25*x^2)'
[-1,1])
holdon
x=-1:
0.1:
1;
y=1./(1+25.*x.^2);
p=polyfit(x,y,3);
xx=-1:
1/5:
yy=polyval(p,xx);
plot(xx,yy,'
--M.'
holdoff
subplot(1,2,2);
1/10:
yy=polyval(p,xx);
三次样条插值:
yy=spline(x,y,xx);
牛顿插值多项式结果:
C=
0.9800-0.3000-0.6250-0.2083-0.5208
P=
26/25-3/10*x+(-5/8*x+1/8)*(x-2/5)+(-3752999689475373/18014398509481984*x+3752999689475373/90071992547409920)*(x-2/5)*(x-3/5)+(-4691249611844317/9007199254740992*x+4691249611844317/45035996273704960)*(x-2/5)*(x-3/5)*(x-4/5)
-0.52080.8333-1.10420.19170.9800
sk=245/2*(-1/5+2*x)*(x-2/5)^2+115*(1-2*x)*(x-1/5)^2+237/56*(x-1/5)*(x-2/5)^2-363/28*(x-2/5)*(x-1/5)^2
sk=
115*(-3/5+2*x)*(x-3/5)^2+405/4*(7/5-2*x)*(x-2/5)^2-363/28*(x-2/5)*(x-3/5)^2-129/8*(x-3/5)*(x-2/5)^2
405/4*(-1+2*x)*(x-4/5)^2+80*(9/5-2*x)*(x-3/5)^2-129/8*(x-3/5)*(x-4/5)^2-771/28*(x-4/5)*(x-3/5)^2
80*(-7/5+2*x)*(x-1)^2+95/2*(11/5-2*x)*(x-4/5)^2-771/28*(x-4/5)*(x-1)^2-1959/56*(x-1)*(x-4/5)^2
实验三:
课本第二章课后上机习题。
(1)
x^(1/2)'
[0,64])
x=0:
64;
y=x.^(1/2);
p=polyfit(x,y,8);
xx=[01491625364964];
—M.'
holdoff
(2)holdon
y=(x).^(1/2);
yy=spline(x,y,xx)
-.r*'
第45页
例8
1/(1+x^2)'
[-5,5])%原图
xx=-5:
1:
5;
y=1./(1+x.^2);
)%样条插值
x=-5:
)%线性插值
[C]=lagran1(x,y)
y=polyval(C,x);
k'
)%拉格朗日插值
x=zeros(1,11);
fork=0:
10
x(k+1)=5*cos((21-2*k)*pi/22);
g'
)%切比雪夫
拉格朗日函数:
function[C]=lagran1(X,Y)
L=ones(m,m);
m
V=1;
ifk~=i不等于
V=conv(V,poly(X(i)))/(X(k)-X(i));
L1(k,:
)=V;
l(k,:
)=poly2sym(V)
C=Y*L1;
L=Y*l
在[0,64]上三次样条插值更精确;
在[0,1]上多项式插值更加精确.
实验四:
利用中点公式求导数
了解并熟练应用中点公式求导数
书本例题
求f=x^(1/2)在x=2处的导数
X=[10.50.10.050.010.0050.0010.00050.0001];
G=zeros(1,n);
G(i)=((2+X(i))^(1/2)-(2-X(i))^(1/2))/(2*X(i));
End
G
x=2;
y=1/2/x^(1/2)
plot(X,G)
G=
Columns1through4
0.366025403784440.356393958692600.353663997049610.35358101950741
Columns5through8
0.353554495459700.353553666807600.353553401641780.35355339335541
Column9
0.35355339070398
0.35355339059327
图形:
实验五:
利用梯形公式,矩形公式,左矩形公式,右矩形公式求解并比较其优劣。
会用梯形公式,矩形公式,左矩形公式,右矩形公式求解
用梯形公式,矩形公式,左矩形公式,右矩形公式求解函数为sin(x)和函数x
函数为sin(x)
function[f1,f2,f3,f4,f5]=g(f,a,b)
symsx;
[A,B]=h(a,b);
[C,D]=h((a+b)/2,0);
f1=int(f,x,a,b);
%原公式
f2=f1-(b-a)*(1/2)*(A+B);
%梯形公式
f3=f1-(b-a)*C;
%矩形公式
f4=f1-(b-a)*A;
%左矩形公式
f5=f1-(b-a)*B;
%右矩形公式
function[A,B]=h(a,b)
f=sym('
sin(x)'
A=sin(a);
B=sin(b);
函数为x
A=0;
B=1;
C=1/2;
>
[f1,f2,f3,f4,f5]=g('
0,1)
f1=
-cos
(1)+1
f2=
-cos
(1)+5217550841117065/9007199254740992
f3=
-cos
(1)+586114737590177/1125899906842624
f4=
f5=
-cos
(1)+713951213746569/4503599627370496
symsx
[f1,f2,f3
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 实验 报告