,,,
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.
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