(0,1) ξ=10-5
x2-0,5=0 .
f()=0. x0=(a+b)/2. f(x0)=0, x0 . f(x0)≠0, f(x0)×f(b)<0 f(x0)×f(a)<0 [ a, 0 ],[ 0, b ], (.. f() ).
x1.
1 f(1)=0 , , f(1)≠0 . . , , , e. f(xk) |ak-bk|.
-
Visual Basic
,
Caption Label1 a=.
Caption Label2 b=.
Caption Label3 eps=.
Caption Label4 =.
Caption Label5 .
Caption Label6 .
Caption Label7 .
Caption CommandButton1 .
:
CommandButton1 :
Private Sub CommandButton1_Click()
a = Val(TextBox1.Text)
b = Val(TextBox2.Text)
eps = Val(TextBox3.Text)
Do
c = (a + b) / 2
If (a ^ 2 - 0.5) * (c ^ 2 - 0.5) > 0 Then
a = c
Else
b = c
End If
Label6.Caption = Label6.Caption & c & Chr(13)
Label7.Caption = Label7.Caption & (a - b) & Chr(13)
Loop While Abs(a - b) > eps
Label5.Caption = c
End Sub
: Run Run
Borland C++
#include <iostream.h>
#include <math.h>
int main() {
float a, b, c;
float eps;
cout << " a, b eps: ";
cin >>a>>b>>eps;
do {
c=(a+b)/2;
if ((a*a-0.5)*(c*c-0.5)>0)
a=c;
else
b=c;
cout << (a+b)/2;
cout << endl;
} while (fabs(a-b) < eps);
cout << c;
cout << endl;
return 0;
}
: Run Run
Borland Delphi ( )
Program z3;
Var a,b,eps,x,f:real;
Begin
Write( a, b eps: );
Readln(a,b,eps);
repeat
c=(a+b)/2;
if (a*a-0.5)*(c*c-0.5)>0 then
a = c
else
b = c;
writeln( c = ,c, (a-b)= ,(a-b));
until abs(a-b)<=eps
writeln( = ,c);
End.
: Run Run
1.
x= φ(x). , x0 , , x0=m. : x1= φ(x0), x2= φ(x1), x3= φ(x2)
..
|
|
|
2. ( )
f()=0. x0 x, : f(x)×f(x)>0. :
xk= xk-1 - f(xk-1) / f(xk-1).
3.
f()=0. x0 x, : f(x)×f(x)>0. : xk= xk-1 - f(xk-1) / f(x0). f(x0) . .
4.
f()=0. :
5.
f()=0. x0=m, 
.
:
.
:
(k+1) - :
.
:
.
.
