matlab应用数值计算误差

解方程组：'x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0'

[x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0')

x =

1

3

y =

-3/2

>>

绘制参数方程：x=sin(p)+p;y=cos(p) 程序内容为：ezplot('x+sin(x)','cos(x)') 绘制成的图形为：

求一个二次方程的根：

>> clear

>> a[3.3,2,3,4,5];

a=[3,5.4,1];

>> x1=(-1*a(2)+sqrt(a(2)^2-4*a(1)*a(3)))/(2*a(1));x2=(-1*a(2)-sqrt(a(2)^2-4*a(1)*a(3)))/(2*a(1));

>> x1,x2

x1 =

x2 =

对于积分 ，数值对比说明舍入误差与算法的数值稳定性的关系。

>> clear

a(1)=0.6321;

for i=2:10

a(i)=1-(i-1)*a(i-1);

end

>> a

a =

Columns 1 through 9

    0.6321    0.3679    0.2642    0.2074    0.1704    0.1480    0.1120    0.2160   -0.7280

Column 10

clear

a(10)=0.0684;

for i=9:-1:2

a(i)=(1-a(i+1))/i;

end

a(1)=0.6321;

>> a

a =

Columns 1 through 9

    0.6321    0.3679    0.2642    0.2073    0.1709    0.1455    0.1268    0.1121    0.1035

Column 10

> E(1)=0.5*10^4;

>> for i=2:9

E(i)=-1*i*E(i-1);

end

>> E

E =

1.0e+009 *

Columns 1 through 8

    0.0000   -0.0000    0.0000   -0.0001    0.0006   -0.0036    0.0252   -0.2016

Column 9

1.8144

>> E(10)=0.1-exp(-1)/10;

for i=9:-1:1

E(i)=-1/(i+1)*E(i+1);

end

>> E

E =

Columns 1 through 8

   -0.0000   0.0000   -0.0000    0.0000   -0.0000    0.0000   -0.0001    0.0007

Columns 9 through 10