, [ a, b ], () e. , e:
(4.1)
, , x0 x1, x2 , .. x0, x1, x2,..., xn ( iteratio ), . , . k :
(4.2)
, .
, , :
(4.3)
:
(4.4)
q > 0 α ≥ 1 , . ³ q a , , , . a, . α = 1 , . α >1, , .
4.2. (쳿)
.
, , ' () .
쳿, , , .
: , 쳿, , .
쳿 ( ) . , .
f(x) = 0 , .
a 0 =a, b 0 =b, x 0 = (a 0 +b 0)/2. , . ,
(4.5)
(4.6)
(4.7)
. , , . , (2)-(4).
(2), (3) , . , .
|
|
. (4.8)
, , (1) e,
. (4.9)
[ c ] - c.
. { xn } f (x). .
:
f (x) ;
ε ;
a, b ( ).
: x f (x) = 0.
':
1. .
2. , c , . , 3.
3. x* c , ( ). . , ( , ), 4; , , , f (x) = 0 c .
4. . , , , .
1 (.4.1). . , b b c: b:= c.
2 (.4.1). . , a a c: a:= c.
1.
, . , f (x). , .
.4.1. .