|
解方程的二分法 matlab 程序 ( x^3-3*x^2+6*x-1=0)
2 K: Q5 ?' s$ r$ d- a6 j* m/ {. n0 x* ?" R1 i- N5 v' N( T
% Bisection.m
+ i7 @+ j8 s9 wfunction[k,x,f_value]=Bisection(f,a,b,eps1,eps2,N)
( `$ q1 W5 Y4 B" u1 H( sfprintf('k ,a ,b ,x, f\n')) B8 W" Y! A9 `
for k=1:N
2 v/ o- E7 X1 |0 ^7 M1 g% B' s x=(a+b)/2;" H+ `& \* T" J6 f5 k. o( F* |" p
f_value=f(x);" T2 B/ `3 a) O
fprintf( '%3d, %10.9f, %10.9f, %10.9f,%10.9f,\n'...
) C+ N! V+ x1 f" ^0 @5 ` ,k ,a ,b ,x, f_value)
! D/ v# K9 W* Q0 L7 r if abs(f_value)< eps1||0.5*(b-a)<eps2
! ]4 j" L4 |4 L/ Z* } A return
' l- |8 N8 {. w# _! i' n1 Y7 v/ q else
+ X8 Q$ a7 H! z, X$ i& m6 n* N if f(x)*f(a)<0* V! e" i# _) K* w' S. k: ~
b=x;' T* h$ }+ M) |/ d( l
else
# w3 X; ?5 m B& Y0 J a=x;
" A$ e8 ~- s. C7 e1 z# ?$ H- i& l end# b5 n6 V( q- w# x5 `7 Y, }3 W
if k== N
' K9 `! i. s8 L warning ('算法超出最大迭代数!') # O5 Q# `0 X: p6 u1 t0 G( ^, b
end( ]; \% D; X( k" a
end
; x: l- S8 q8 l1 O: B; S) Y$ H
' ^4 i$ H* }) r4 A- x( c; j% examlpe7.m: t! i4 T' Y0 ]5 }
a=0; b=1;
" _. B8 x7 M5 t, beps1=1e-4;eps2=1e-4;
0 _, m" t) H9 b: Z9 F: Q1 T N=300;
8 J( O! m) }9 m& a, O" u& Vf=@ (x) (x^3-3*x^2+6*x-1); X" i/ f8 n' A- m5 K9 T9 L$ l; Y
Hfun=@Bisection;. M+ r' l8 k" J) r2 U' o
[k,x,f_value]= feval(Hfun, f,a,b,eps1,eps2,N);9 N3 s7 Z7 x/ t+ I/ p* b' S
8 I$ [! y K5 V. ^- s7 f
运行结果' ~0 O: H) Q" I0 e
>> examlpe7" g; k G( G. ~5 y( ?
k ,a ,b ,x, f. I4 c% M! _, c
1, 0.000000000, 1.000000000, 0.500000000,1.375000000,
& u' c& l+ j. Z. H- X5 k5 C 2, 0.000000000, 0.500000000, 0.250000000,0.328125000,* `# k5 e/ b/ B6 Y6 X3 p6 m6 f
3, 0.000000000, 0.250000000, 0.125000000,-0.294921875,3 I# y5 U- j' A* H8 w: g1 Y) t" O/ m
4, 0.125000000, 0.250000000, 0.187500000,0.026123047,
4 G' e1 h8 g. B1 u$ y 5, 0.125000000, 0.187500000, 0.156250000,-0.131927490,
6 l/ Z8 }( k9 |0 p$ q& i 6, 0.156250000, 0.187500000, 0.171875000,-0.052295685,
0 ?& X: l: O: H. L" `% m 7, 0.171875000, 0.187500000, 0.179687500,-0.012936115,
o7 m5 w3 p( ^( v9 k0 P 8, 0.179687500, 0.187500000, 0.183593750,0.006630838,: H! m8 V4 E9 J o; d0 ?
9, 0.179687500, 0.183593750, 0.181640625,-0.003143273,. `3 n X, I0 ^- f, W( R
10, 0.181640625, 0.183593750, 0.182617188,0.001746121, r% o3 Y5 T. @! L
11, 0.181640625, 0.182617188, 0.182128906,-0.000697991,5 j9 B9 ] S5 X" s- G
12, 0.182128906, 0.182617188, 0.182373047,0.000524211,
, w. O% A: ?8 Y1 S# S+ m0 N. B" {( Y; ] 13, 0.182128906, 0.182373047, 0.182250977,-0.000086854,
4 R% B" V; U* n% {' ?) M$ g, o1 \
! _# _1 K8 {! x- G, J
: m& |- x, Z+ k% j9 ? |
|