:
1. a b, .
2. [a,b] .
3. , ( ).
4. .
- :
. 4.
, .
:
1. , .
2. [xmax-dx, xmax+dx] , , dx/10.
3. .
max1 dx max2 dx/10. |max2-max1| <=E ( ), max2 , , , .2.
, .
:
. 5.
, x x+∆x ∆x = const F(x). F(x n+1)>F(xn), x . F(xn+1) F(x) . .
:
1. x=x₀ F(x) F(x₀). D=h, h=∆x .
2. , G=F(xn), F(xn)=F(x₀), x=x+D F(x n+1)=F(x).
3. F(x n₊₁)>G; , .2, , .4.
4. D=-D/4. |D|>E/4, E xn . , .2, .. 4 . , .
( [a, b] ) :
1. |b-a|<2E, E xn. , .6; , .2.
2. [a, b] ,
|
|
x=(a + b)/2
x1=(a + b - E)/2 x2=(a + b + E)/2
3. x F(x₁)>F(x₂).
4. F(x₁)>F(x₂). , b=x₂ .1. , .5.
5. a=x₁ .1.
6. xn=(a+b)/2 F(xn).
( ). .
, () N. , , , . , , :
FN=FN-1+FN-2
F0=F1=1
:
1) , . 1=X₀/FN, l, , X₀. , X₀ 1, FN,
N .
2) X0 FN-2 b.
3) . > , [ , FN] .
4) , = .
5) 3 .., , , .
. 6 :
. 6. .
N l, .
, (. 7).
. 7
[a, b] F(x), , .
:
1. k=(√5-1)/2 [a, b].
2. 1=a + (1-k)*(b-a) F(x1).
3. 2=a + k*(b-a) F(2).
4. |x2-x1|<E, E xn. , xn = (x1+ x2)/2 F(xn), xm F(xn). , .5.
5. F(x1) < F(x2). , , = 1, 1 = 2 F(x1) = F(x2), .3. .4.
F(x1) ≥ F(x2), b = x2, x2 = x1, f(x1) = f(x2), .2 .4