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解方程的二分法 matlab 程序 （ x^3-3*x^2+6*x-1=0）
% j) R' I2 e0 R7 O. J; L, P# d; O2 l! R
% Bisection.m
7 D. x2 m% A& Z. Z8 _* j" Z: Z9 }function[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
% Y& E; A! D7 U* Afprintf('k ,a ,b ,x, f\n')
$ b9 p8 Q' P/ R- R/ _% ffor k=1:N; q) d" N4 p$ H$ |) _' O' y
x=(a+b)/2;
' u8 Y% s$ Q( H% d5 R4 y f_value=f(x);6 ]8 n" p) A6 F# V& B" z2 i
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...2 H" h4 {4 M( ?* g& v
,k ,a ,b ,x, f_value)- i' i) R5 f0 z4 l: S" U
if abs(f_value)< eps1||0.5*(b-a)<eps2
! k# X$ H' S! m8 N% u return
/ U% P* ]$ f5 D0 u9 H9 r" p+ ?2 z& F else
# E' _* p% ~/ w* U) @, U if f(x)*f(a)<0
! ^' }# L( O# |, G% s' c b=x;7 N7 ^% N0 Q3 C" m+ |( D3 Z5 j
else* {6 }) V6 Q; A! b( K8 Q) R
a=x;
( s4 a& V, u* D0 q# k+ P. ^+ _; [ end% b7 I7 \8 l+ _+ p) g
if k== N
; [9 x$ w2 F+ g2 ?+ u' x warning ('算法超出最大迭代数!')
/ a! g7 U) H) X8 R$ v. ` end
0 |) t P& o: I/ Q1 v; f8 N end
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% examlpe7.m9 ^9 e/ o$ t4 B5 M
a=0; b=1;
: V% X2 }# q* A/ T) [% {7 |eps1=1e-4;eps2=1e-4;
6 I6 x. C* O2 ?' I$ H7 u7 \9 W N=300;) ?7 V! Z: _8 j# `$ U: ~
f=@ (x) (x^3-3*x^2+6*x-1);
& P9 S# }+ f PHfun=@Bisection;
3 T, ` X v- [ w& P1 ^[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);9 ?1 T, T7 v6 E, D1 L* _- ^* x+ m
3 ^" k" I# v5 [" m5 W& W {
运行结果
5 A8 [! C% V; y- c" L* C; e1 G/ n>> examlpe77 F: `6 }3 s3 l) k; l7 C
k ,a ,b ,x, f. T) w3 C8 {' o L+ I4 |& B8 m" {
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
4 r5 e" t, C: i) T 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,
% o, C6 ?$ D' f0 O! W: C1 z T 3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,& v$ ?8 L; I. O( @7 K+ A' e& x
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
F7 B+ j3 a- V0 N 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,6 K0 B) \( B, k7 D0 s( x+ E
6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
/ C6 c3 t( o, L ?. G 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
. Y& y. S+ ?! x/ Q7 ` 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,
/ z% u. Q2 i! P4 p4 E: ` 9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,
% d0 v* C+ E+ t6 y& f/ _* M! N6 E 10, 0.181640625, 0.183593750, 0.182617188,0.001746121,
! i0 s; B3 w# q- z7 | 11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,
/ t# @- H% A! }7 T+ p 12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
) d# Y4 Z9 A& D 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,( N( Z" h$ R2 Q- Q5 T' i+ ?
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发表于 2015-6-4 09:25:35