实验五 MATLAB 在数值计算中的应用
徐晓-应用数学10-3班-10104479
实验目的
在工程技术中，大量的实际问题都需要进行近似处理，从而产生不同问题的数值计算 方法。而 MATLAB 具有强大的数值运算功能，本实验的目的是学会用 MATLAB 软件进行一些数值运算，包括代数方程求根、插值问题和曲线拟合问题等。
实验内容
一、代数方程求根
1、求方程x?x?6?0的根。 先画图观察根的个数及大概位置。 输入命令 ：
>> fplot('[x^2+x-6,0]',[-10,10])
2结果如下图
从图中可看出方程在[-2,0]及[4，6]区间上各有一根， 再输入命令 ：
>> x1=fzero('x^2+x-6',[-4,-2])
x1 = x2 =
2 -3
>> x2=fzero('x^2-4*x-5',[0,4])
2、求方程3cosx?lnx的所有的根
fplot('[3*cos(x)-log(x),0]',[- 50,50])%先画图，看一下确定解得大致范围 fplot('[3*cos(x)-log(x),0]',[- 30,30])%通过图形确定解得具体范围
f=inline('3*cos(x)-log(x)');
fsolve(f,[-19.04,-18.62,-13,-12,-7.2 ,-5.2,-1.4,1.4,5.2,7.2,12,13,18.62,19.04])%利用单个解得最近数值进行求解。 结果为：
ans =
Columns 1 through 4
-19.7669 + 1.0760i -19.7669 + 1.0760i -13.5544 + 1.0312i -13.5544 + 1.0312i
Columns 5 through 8
-7.3921 + 0.9647i -7.3921 - 0.9647i -1.4453 + 0.7984i 1.4473 - 0.0000i
Columns 9 through 12
5.3020 + 0.0000i 7.1395 + 0.0000i 11.9702 - 0.0000i 13.1064 + 0.0000i
Columns 13 through 14
18.6247 - 0.0000i 19.0387 + 0.0000i
4323、求方程x的所有的根。 ?115x?1575x?7625x?12500?0fplot('[x^4-115*x^3+1575*x^2-7625*x+12500,0]',[-1000,1000])%先画图，看一下确定解得大致范围
fplot('[x^4-115*x^3+1575*x^2-7625*x+12500,0]',[-40,120])%通过图形确定解得具体范围
f=('x^4-115*x^3+1575*x^2-7625*x+12500'); fsolve(f,[5])%求出5附近的根
fsolve(f,[100])%求出100附近的根 结果为：
ans = 5 ans = 100
22??2x?y?3y?24、 求方程组?的解。
22??4x?2y?5x?3[x,y]=solve('2*x^2-y^2+3*y=2','4*x^2+2*y^2-5*x=3')
x= vpa(x,2) y= vpa(y,2)
结果为：x =
4/5*(3/4+1/16*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+1/16*i*((-120*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+120*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2))^2-7/10-3/40*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-3/40*i*((-120*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+120*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2)
4/5*(3/4+1/16*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-1/16*i*((-120*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+120*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2))^2-7/10-3/40*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+3/40*i*((-120*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)+10*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+120*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1
/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2)
4/5*(3/4-1/16*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+1/16*10^(1/2)*((12*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+12*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2))^2-7/10+3/40*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-3/40*10^(1/2)*((12*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+12*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2)
4/5*(3/4-1/16*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-1/16*10^(1/2)*((12*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+12*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2))^2-7/10+3/40*10^(1/2)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+3/40*10^(1/2)*((12*(81+4*410^(1/2))^(1/3)*((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)*(81+4*410^(1/2))^(2/3)-((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2)+12*10^(1/2)*(81+4*410^(1/2))^(1/3))/(81+4*410^(1/2))^(1/3)/((6*(81+4*410^(1/2))^(1/3)+(81+4*410^(1/2))^(2/3)+1)/(81+4*410^(1/2))^(1/3))^(1/2))^(1/2) y =