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1.

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2.2

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4.

5.

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a0xn+a1xn-1+...+an-1x+an=0, a0¹0

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f() =0,

- f(), 䳺 , . .

() .

˳ - .

1.

:.

, , (, ). , F(X) [;][].

, F(X), - X0, .

.

.

1.

, [-0.4,0].

=f(), .

:.

2.

.

.

3

= (),

1 .

2 .

3 .

2.

2.1

f()=0 (2.1)

X[a, b]. (2.1) :

=φ (). (2.2)

, . :

=g() f() + ≡ φ (),

g() - , [a, b].

(0)- - ( (0)=(+b)/2). :

(k+1)=φ ((k)), k=0, 1, 2,. .. (2.3)

(0).

: 1 {(k)} φ , =φ ()

: .

(2.4)

(k+1)=φ ((k)) (2.4), φ (2.4).

*=φ (*). , *- (2.2), . . X=*.

{(k)}. :

2.1: ( ) =φ () [a, b] :

1) φ () C1[a, b];

2) φ () [a, b] " [a, b];

3) q > 0: φ '() ≤ q < 1 [a, b]. {(k)}, (k+1)= φ ((k)), k=0, 1,. .. - (0)[a, b].

: {(k)}: (k)= φ ((k-1)) (k+1)= φ ((k)) 2) (k) (k+1) [a, b], :

(k+1)- (k)= φ ((k)) - φ ((k-1)) = φ '(ck)((k)- (k-1)),

ck((k-1), (k)).

:

(k+1)- (k) = φ '(ck) (k)- (k-1) ≤ q (k)- (k-1) ≤

≤ q (q (k-1)-)( (k-2)) = q2 (k-1)- (k-2) ≤ ... ≤ qk (1)- (0). (2.5)

S∞= (0)+ ((1)- (0)) +. .. + ((k+1)- (k)) + .... (2.6)

, ,

Sk= (0)+ ((1)- (0)) +. .. + ((k)- (k-1)).

,

Sk= (k)). (2.7)

, {(k)}.

(2.6) ( (0))

q0 (1)- (0) + q1(1)- (0) +. .. + (1)- (0) +. .., (2.8)

( q < 1). (2.5) (2.6) (, 2.8) ( (2.8) (2.6). (2.6) . {(0)}.

,

X - (k+1)

.

X - (k+1)= X - Sk+1= S∞- Sk+1= ((k+2)-)(k+1) + ((k+3)-)( (k+2)) +. ...

X - (k+1) ≤ (k+2)-(k+1) + (k+3)- (k+2) +. .. ≤ qk+1(1)- (0) + qk+2(1)- (0) +. .. = qk+1(1)- (0) / (1-q).

X - (k+1) ≤ qk+1(1)- (0) / (1-q). (2.9)

(0) (k), (1)- (k+1)( ) , qk+1≤ q :

X - (k+1) ≤ qk+1(k+1)- (k) / (1-q) ≤ q(k+1)- (k) / (1-q).

, :

X - (k+1) ≤ q(k+1)- (k) / (1-q). (2.10)

. =φ () , ε,

X - (k+1) ≤ ε.

(2.10) , ε ,

(k+1)-(k) ≤ (1-q)/q. (2.11)

, =φ () , ε (1-q)/q.

2.2: q .

2.2

. , - :

3.

- .

4.

. 0, . . , :

5.

3. -

- 6, 7.

, :

FN, F - ;

X, START - ;

, PRECISION - ;

N, COUNT_ITER - .

6 - SIMPLE_ITER

7 -

4.

SIMPLE_ITER.txt;

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( SIMPLE_ITER (NE X FN)

(D

(AND ( < = N 0)>< ( > (ABS (- (FUNCALL FN X) X)) (* (FUNCALL FN X)))) X)><

( (SIMPLE_ITER (- N 1) (FUNCALL FN X) FN))

)

);

"

(LOAD D:\\FUNCTION.TXT");

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(SETQSTART (/ (- (CADRINTERVAL) (CARINTERVAL)) 2));

><

(SETQ ROOT (SIMPLE_ITER COUNT_ITER PRECISION START (FUNCTION F)));

>< "

(SETQ OUTPUT_STREAM (OPEN D:\\ROOT.TXT": ><DIRECTION: ><OUTPUT)><);

(PRINT 'ROOT OUTPUT_STREAM)

(PRINT ROOT OUTPUT_STREAM);

><

(TERPRI OUTPUT_STREAM)

(CLOSE OUTPUT_STREAM)

FUNCTION.txt ( 1);

>< ֲ

(EFUN F (X)

(/ (+ (- (* X X) (* 5 (COS X))) 3.25)>< 3)

);

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(SETQ COUNT_ITER 100);

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(SETQ INTERVAL '(-0.4 0)><);

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(SETQ PRECISION 0.0001)><

FUNCTION.txt ( 2);

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(FUN F (X)

(- (* X X) (COS X))

);

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(SETQ COUNT_ITER 60);

>< ̲, в

(SETQ INTERVAL '(1 1.5)><);

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(SETQ PRECISION 0.0001)><

5.

1.><

8 -

9 -

2.><

10 -

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, , . >< , , - .><

ϳ .>< , .>< .>< .>< .><

1.>< , . . [] / . . , . . .>< - .><: , 2007.>< - 708 .><

2.>< , . . :>< .>< [] / . . , 3- - .><: -, 2006.>< C. 412.><

3. , . . .>< [ ] / . . .>< - .><: , 2001.>< . 504>.

4.)( [ ] - :)( http://solidbase.karelia.ru/edu/meth_calc/files/12.shtm

5. , . . .)( [] / . . , . . .)( - .)(: , 2006.)( C. 346.)(

6. , . . [] / . . , . . , . . .)( - :)( , 2002.)( - 160 .)(

7.)( , . . Lisp.)( [ ] / . . , . . .)( - .)(: , 2003.)( . 79.)(

8. . ̳ ˳ [] / . , . .)( - .)(: , 1990.)( - 460 .)(

))))