. , , ,

,,,

(-) — ,

1.

2.

2.1

2.2

3. -

4.

5.


( ) () . , (16431727), .

De analysi per aequationes numero terminorum infinitas (. ), 1669 , De metodis fluxionum et serierum infinitarum (. ) Geometria analytica (. ) , 1671 . , , ( ). : 1711 , 1736 . : . xn, x.

1685 , . 1690 Analysis aequationum universalis (. ). , xn , . , 1740 , . , .

1879 The Newton-Fourier imaginary problem (. -) , . .

.


1.

:

.

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

, F(X), - X0, .

Xi, Xi+1 . F(X) X = Xi, . Xi+1 , .

:

Xi+1 = Xi - F(Xi) / F'(Xi)

, F(X) "", Xi , Xi+1 .

1.

, .

.


,

-9.716215;

5.74015;

3.401863;

-2.277028;

1.085197;

0.766033;

0.739241.

,

0.739241.

2.

cosx = x3.


f(x) = cosx − x3.

.

x x3 > 1 x > 1, , 0 1. x0= 0.5, :

1.112141;

0.90967;

0.867263;

0.865477;

0.865474033111;

0.865474033102.

,

cosx = x3 0.86547403.

3.

, .

.

,

-2.3;

-2.034615;

-2.000579;

-2.0.

,

-2.


2.

2.1

x [a, b], . n

,

.

, (1)

. , :

.

,

.

(1), ( )


. (2)

, . , , ( 1).

, , , . B0 .

1.

x Ox. , x ..

, , B0, , .


.

a , , , , ..

.

n

.

[a, b], . ,

,

.. .


.

, . :

.

x. , , .

2.2

.

.

. . , . , . .

2. ,

, .

, .

, , , .

.

. , , .


3. -

- 3, 4.

:

FUNCTN, FX ;

DFUNCTN, DFDX ;

A ;

START, X0 ;

PRES, E .

3


4 - NEWTOM


4.

FUNCTION.txt ( 1)

; COSX - X3

(DEFUN F(X)

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

)

; -sinx-3x2

(DEFUN DFDX (X)

(- (* -1 (SIN X)) (* 3 X X))

)

(SETQ X0 0.5)

(SETQ E 0.0001)

FUNCTION.txt ( 2)

; x-cosx

(DEFUN F(X)

(- X (COS X))

)

; 1+sinx

(DEFUN DFDX (X)

(+ 1 (SIN X))

)

(SETQ X0 -1)

(SETQ E 0.0001)

FUNCTION.txt ( 3)

; X2+2X

(DEFUN F(X)

(+ (* X X) (* 2 X))

)

; 2X+2

(DEFUN DFDX (X)

(+ 2 (* 2 X))

)

(SETQ X0 -2.3)

(SETQ E 0.0001)

NEWTON.txt

;

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

;

(DEFUN NEWTOM (START PRES FUNCTN DFUNCTN)

;

(DECLARE (SPECIAL X))

(DECLARE (SPECIAL A))

;

(SETQ X START)

(SETQ A (/ (FUNCALL FUNCTN X) (FUNCALL DFUNCTN X)))

(LOOP

(SETQ X (- X A))

(SETQ A (/ (FUNCALL FUNCTN X) (FUNCALL DFUNCTN X)))

;

(IF (<= (ABS A) PRES) (RETURN X))

)

)

;

(SETQ OUTPUT_STREAM (OPEN "D:\KOREN.TXT" :DIRECTION :OUTPUT))

;

(SETQ KOREN (NEWTOM X0 E (FUNCTION F) (FUNCTION DFDX)))

;

(PRINT 'KOREN OUTPUT_STREAM)

(PRINT KOREN OUTPUT_STREAM)

;

(TERPRI OUTPUT_STREAM)

(CLOSE OUTPUT_STREAM)


5.

1.

5 .

6 .

2.

7 .


8 .

3.

9 .

10 .


, , . , , .

. , . .


1.         , .. [] / .., ... .: , 2007. 708 .

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

3.         , .. . [ ] / .. . .: , 2001. . 504.

4.    [ ] : http://ru.wikipedia.org/wiki/_

5.         , .. . [] / .., ... .: , 2006. C. 346.

6.         , .. [] / .., .., ... : , 2002. 160 .

7.         , .. Lisp. [ ] / .., .. . .: , 2003. . 79.

8.         . [] / ., .. .: , 1990. 460 .

1. 2. 2.1 2.2 3. - 4.

 

 

 

! , , , .
. , :