4.1 (1)
clear x0=1.5; x1=1+1/x0^2;
while abs(x1-x0)>=0.00005 x0=x1; x1=1+1/x0^2; end x1
结果：收敛 x1 =
1.4656 (2)
clear x0=1.5;
x1=(1+x0^2)^(1/3); while abs(x1-x0)>=0.00005 x0=x1;
x1=(1+x0^2)^(1/3); end x1
结果：收敛 x1 =
1.4656 (3)
clear x0=1.5;
x1=(1/(x0-1))^(1/2); while abs(x1-x0)>=0.00005 x0=x1;
x1=(1/(x0-1))^(1/2); end x1
结果：MATLAB始终正忙，不收敛 4.2...
>> x1=roots([1 -2 -4 -7]) x1 =
3.6320 -0.8160 + 1.1232i
-0.8160 - 1.1232i
>> x2=fzero('x^3-2*x^2-4*x-7',3) x2 =
3.6320
>> s='x^3-2*x^2-4*x-7' s =
x^3-2*x^2-4*x-7
>> x=solve(s) x =
1/6*(1108+36*745^(1/2))^(1/3)+32/3/(1108+36*745^(1/2))^(1/3)+2/3
-1/12*(1108+36*745^(1/2))^(1/3)-16/3/(1108+36*745^(1/2))^(1/3)+2/3+1/2*i*3^(1/2)*(1/6*(1108+36*745^(1/2))^(1/3)-32/3/(1108+36*745^(1/2))^(1/3))
-1/12*(1108+36*745^(1/2))^(1/3)-16/3/(1108+36*745^(1/2))^(1/3)+2/3-1/2*i*3^(1/2)*(1/6*(1108+36*745^(1/2))^(1/3)-32/3/(1108+36*745^(1/2))^(1/3))
>> vpa(x) ans =
3.6319808055660635175221064455414 -.81599040278303175876105322277063+1.1231574348390212417188459351214*i -.81599040278303175876105322277063-1.1231574348390212417188459351214*i
4.3............
>> roots([1 2 10 -20])
ans =
-1.6844 + 3.4313i -1.6844 - 3.4313i 1.3688
4.4.....
>> x=solve('1-x-sin(x)') x =
.51097342938856910952001397114508
>> x=fsolve('1-x-sin(x)',0.5)
Optimization terminated: first-order optimality is less than options.TolFun. x =
0.5110
4.5......
>> x=fsolve('x-sin(x)/x',1)
Optimization terminated: first-order optimality is less than options.TolFun. x =
0.8767
4.6.......
>> ezplot('sin(x)+1-x^2/2'),grid,hold Current plot held >> ezplot('x-x')
>> x=fsolve('sin(x)+1-x^2/2',-0.8)
Optimization terminated: first-order optimality is less than options.TolFun. x =
-0.7750
>> x=fsolve('sin(x)+1-x^2/2',2)
Optimization terminated: first-order optimality is less than options.TolFun. x =
1.9619
4.7．。。。。
>> ezplot('cos(x)-0.5-sin(x)'),grid,hold Current plot held >> ezplot('x-x')