文档介绍：= ,其中E, R, 0, S分别为单位矩阵、随机矩阵、零矩阵和对角矩阵,试通过数值计算验证A2 = .
程序:
E=eye(3);R=rand(3,2);O=zeros(2,3);S=diag([1,2]);A=[E,R;O,S]; ...
B=A*A,C=[E R+R*S;O S*S],a=B==C
结果:
B =
0 0
0 0
0 0
0 0 0 0
0 0 0 0
C =
0 0
0 0
0 0
0 0 0 0
0 0 0 0
a =
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
用命令magic(n) 生成幻方矩阵,通过计算研究它的性质,如行和、列和、两条对角线和等(可以利用命令diag, sum, fliplr, flipud,其用法可以查阅MATLAB帮助系统).
程序:
A=magic(4),s1=sum(A),s2=sum(A'),...
s3=sum(diag(A)),s4=sum(diag(fliplr(A)))
结果:
A =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
s1 =
34 34 34 34
s2 =
34 34 34 34
s3 =
34
s4 =
34
设y1 = –1/(1+x2),y2 = exp(–x2/2),y3 = sin(2x),y4 =,x在
[–2, 2]内适当离散化,计算y1 + y2,y1y2,y3/y2,(5y4 – y1)/y22.
程序:
x=-2::2;y1=-1./(1+x.^2);y2=exp(-x.^2/2);y3=sin(2*x);y4=sqrt(4-x.^2);
>> a=y1+y2,b=y1.*y2,c=y3./y1,d=(5*y4-y1)./y2.^2
结果:
a =
- 0 -
b =
- - - - - - - - -
c =
- 0 - - -
d =
,a2,…,an » 0,a1远大于an,用从1到n和从n到1两种顺序计算 ak,观察哪个更准确些,分析原因。
程序与结果:
>> syms x
>> symsum(1/x,1,100)
ans =
14466636279520351160221518043104131447711/27888150091884990865813523574**********
>> symsum(1/x,100,1)
ans =
-291248328005999177069358804052937859600407/697203752297124771645338089353**********
= ò01xnex–1dx ( n = 0, 1, 2, …) 证明如下递推公式:
I0 = 1 – e–1, In = 1 – nIn–1, n = 1, 2, ….
用递推公式计算I1, I2, …, In,观察n多大时结果就不对了(考虑一个简单的判断结果错误的标准),,即
In–1 = ( 1 – In )/n .
从In倒过来计算In–1, …, I1, I0,而In由下式估计
(ex–1) = In(1) < In < In(2) = (ex–1).
不妨取In = ( In(1) + In(2) )/n,将计算结果与前面的进行比较,得到什么启发.
,x3,x4,x5的图形,如一个图上画几条曲线,