华科数值方法习题

Exercise-1for Numerical Methods

Deadline:2016-10-2

1.P23:1

2.P23:9(a)

1/10=0.00011two-0.0001100two=0.000000011two=1/(1-2^-4)×(2^-8+2^-9)=0.00625

3.P23:13(c)

C:3/17=0.10112×2-2

1/9=0.11102×2-3=0.011102×2-2

3/17+1/9=1.001×2-2

1/7=0.10012×2-2

(3/17+1/9)+1/7=1.10112×2-2=0.11102×2-1

4.Find the error E x and relative error R x.Also determine the number of significant digits in the approximation:

(a)x=2.71828182,x’=2.718276;

(b)y=83500000,y’=83499998;

(c)z=0.000068,z’=0.00006666666.

(a):E x=|x-x’|=0.00000582

R x=E x/|x|=2.141058×10-6

R x<101-d/2

d=6

(b)E y=|y-y’|=2

R y=E y/|y|=2.39521×10-8

R y<101-d/2

d=8

(c)E z =|z -z’|=0.00000133334R z =E z /|z|=0.019607941R z <101-d /2

d =2

5.P37: 2.

会出现截断误差（Truncation error ）4/107534/10642

|

)

421031()!3!21(x x x x dx x x x +++=+++?=0.2553074428013396.P37:6(a)

P(2.72)=2.723-3×2.722+3×2.72-1

=20.12-3×7.398+8.160-1=20.12-22.19+8.16-1

=5.090

4

Q(2.72)=((2.72-3)×2.72+3)×2.72-1

=(-0.7616+3)×2.72-1

=2.238×2.72-1

=6.087-1

=5.087

R(2.72)=(2.72-1)3

=1.723

=5.088

7.P37:13(b,d).

(b)=-+-=4

0001.100000001.100002

x 21-1.00000000000×10-4=---=4

0001.100000001.100002

x 22-9.99999997977×103(d)=-+-=4000001.1000000000001.10000002x 21-1.00000000000×10-6

=---=4

000001.1000000000001.10000002

x 22-9.99992385565×105

8.P39:2

format long

clear,clc

n=[0:10]';

x=[];r=[];p=[];p=[]; %%%%%%%%%%%%x数列%%%%

x=[0.5.^(0:10)]'; %%%%%%%%%%%%r数列%%%%

ri=0.994;

r=[ri];

for i=1:10

ri=ri*0.5;

r=[r,ri];

end

r=r'; %%%%%%%%%%%%%p数列%%%%

pi=1;

pj=0.497;

p=[pi,pj];

for j=1:9

pn=1.5*pj-0.5*pi;

p=[p,pn];

pi=pj;

pj=pn;

end

p=p'; %%%%%%%%%%%%%%q数列%%%%%% qi=1;

qj=0.497;

q=[qi,qj];

for k=1:9

qn=2.5*qj-qi;

q=[q,qn];

qi=qj;

qj=qn;

end

q=q'; %%%%%%%%%%%%%%%%%数据导入到xls表格%%%% A=[n,x,r,p,q];

xlswrite('AAA.xls',A);

B=[n,x-r,x-p,x-q];

xlswrite('AAA.xls',B,'sheet2'); %%%%%%%%%%%%%%%%%绘图%%%%%%%%%%%%%%%% figure(1);

m1=x-r;

m1(1,:)=[];

n1=n;

n1(1,:)=[];

plot(n1,m1,'*');

xlabel('n');

ylabel('xn-rn');

title('误差序列{xn-rn}');

axis([01000.0035]);

grid on; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(2);

m2=x-p;

m2(1,:)=[];

plot(n1,m2,'*');

xlabel('n');

ylabel('xn-pn');

title('误差序列{xn-pn}');

axis([01000.006]);

grid on; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% figure(3);

m3=x-q;

m3(1,:)=[];

plot(n1,m3,'*');

xlabel('n');

ylabel('xn-qn');

title('误差序列{xn-qn}');

axis([01002.5]);

grid on; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%