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解方程的二分法 matlab 程序 ( x^3-3*x^2+6*x-1=0)
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7 K$ g2 C# [' A1 n& }, Q% Bisection.m
) F' V& P2 S% [5 P3 l/ T/ C) Ifunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
: x T: V" N9 g5 w7 mfprintf('k ,a ,b ,x, f\n')
2 |% I: u* ^. v1 tfor k=1:N, L2 t1 a" ~6 F0 O$ p* N
x=(a+b)/2;
C! ~ \ p3 a f_value=f(x);
3 G' L$ W: x) y2 E) R4 M fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...4 D! M) H2 h% p4 `" R
,k ,a ,b ,x, f_value)+ O1 S% ] ^9 T( {
if abs(f_value)< eps1||0.5*(b-a)<eps2
) G1 T8 z3 N q/ m' k# i! _ return- | `+ F2 ?1 c7 ^* }; ^' k
else+ _6 X2 R7 z7 o3 X5 I+ z- E% f
if f(x)*f(a)<09 A8 ?; `& {4 ?
b=x;
# T/ o3 b) m! j# z; }. t5 f else
9 }: e" \* v* w4 Q/ X( c2 X( P$ W a=x;* x- a7 ^) w% W5 ~. b2 r
end; Q! E9 _2 v. V: o
if k== N% m- V' z: v1 B/ e. ?2 B
warning ('算法超出最大迭代数!')
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end
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% examlpe7.m
' m! n M. z- a9 V" y" w% |a=0; b=1;; D- K- x O2 X$ g( y
eps1=1e-4;eps2=1e-4;% }; Z( _8 A' Y* @5 m
N=300;
; `" w2 _* n$ E& T8 q8 l% af=@ (x) (x^3-3*x^2+6*x-1);
. s6 H% w5 _4 ~- w) E; MHfun=@Bisection;
" O* A9 L8 \1 a7 R. U[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);; `, W4 ]4 |& E$ G- v" ?
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运行结果( C0 W0 b. p. y Z6 m. Z, r
>> examlpe7
. k( A* i4 \! U8 A! H" Y4 M$ jk ,a ,b ,x, f# |) J$ ]% K* Z
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
+ o. `; I2 g% q% y* n5 T8 l 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
; b' C7 ?$ c3 @- j }- \. Z& v 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,
; S, M- k+ E! L" z% J$ g 4, 0.125000000, 0.250000000, 0.187500000,0.026123047,3 S; q. l* ^4 L+ c
5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,1 ]3 t2 h, l; p6 p' `
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
( b8 W1 V( D q. r0 L- ?. t 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,# Y: w0 J( S! m. y, ]
8, 0.179687500, 0.187500000, 0.183593750,0.006630838,7 E' t- _0 F7 i2 f. w7 T1 u
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,$ `& x* H1 ]( ]
10, 0.181640625, 0.183593750, 0.182617188,0.001746121,6 @( i3 R: Q6 p5 z- f. a4 z
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,2 B' w0 Z$ G3 i$ e2 D
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
! B+ R; L( R5 s; X$ P. t 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
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