[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close
) R: B1 I S6 I
% n=input('请输入迭代次数：');7 u& X, n2 T; O! A# Q* ~& l
% qujian=input('请输入初始区间：');( l, G1 ^# m; M' m8 \) s H4 M$ B- A
n=100;
4 l# J! O8 v8 M! f
wucha=0.005;
. Z8 l) y* L( {
qujian=[0 1];\" ]! o3 j9 O# X$ G8 H\" o
a(1)=qujian(1);; j/ Q% k$ K. g7 g0 ]& Q
b(1)=qujian(2); / T6 w9 R4 i3 H2 l
a0=a(1);
: F# s5 \: N\" K, F
b0=b(1);
\" ?* T7 d @. H3 Q) R' u
x=qujian;
! U6 x5 u, g, \ ?\" p$ G
y=exp(x)+10*x-2;- A/ l3 a4 x! w2 P4 T
y1=y(1); %小于05 L$ w2 f( u* u: ~3 \- F
y2=y(2); %大于0
+ y) Y* ]5 U2 m: V! B% V
for i=1:n %总迭代次数
1 q4 b' ^6 m: `\" I% |% Z3 m0 j
c(i)=(a+b)/2;4 S& b) r I. u! k( `
f(i)=exp(c(i))+10*(c(i))-2;) N& x! Y# h- k' o
kesai_k(i)=(b-a)/2;
% Z# @9 i3 V3 i# a/ z- Q; q$ v
if f(i)>0+ n1 g8 ]& w4 a Q8 H
b=c(i);/ w$ o* Z' O5 I\" U! ?' q% F( \' G, t# y
b1(i)=c(i);
2 ~' F$ h8 o6 |/ z0 A! K4 R
a1(i)=a;
elseif f(i)<0' o& [9 c3 v8 }( F! y% {
a=c(i); v# `7 S( v* g; U9 {
a1(i)=c(i);( Q2 `* n; B' i, {2 S7 ?. c9 u
b1(i)=b;% `* \) U# k8 p6 F, B! c\" J0 x0 X
elseif f(i)==0||kesai_k(i)<=wucha* f J* I$ X3 [- n0 C; i
disp('精确值解为：');
# f# o6 I( ^4 p% o
disp(c(i));
% p; ]$ j2 D( I+ p1 U1 w! _
break;
) [. h! ~, U! p+ x) I
end8 u2 F& x! U$ |' F. U
end
& ~; u; e: k1 a8 n* X P
disp('迭代次数：');
\" k9 o4 Y/ I4 e0 a3 d, r
fprintf('%d次\n\n',n);
( p5 R7 Z* [* e r' Q
fprintf('要求误差%f\n\n',wucha);8 ]\" S- [1 J\" S0 E
disp('输出矩阵为：');
; s: {# l\" p& S$ H1 Q
A=[a0 a1]';$ Q5 _; N5 |2 Q
B=[b0 b1]';! L! u* b! \6 } h
format long' w' ?% J, W3 A
data_out=[A B c' f' kesai_k']
- p( Y( A/ t+ J+ g. g5 L# o0 d
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：' ^/ p* e. K3 R. L8 ?( {9 Z8 P9 d
0.0905
3 z' w$ l) ~* `1 g6 L6 Z\" W9 T; v: @
4 u0 @6 A% K/ A2 g
迭代次数：
- `- A: u8 i- ~' f3 q# P. k$ e
100次
; ^/ q1 X5 U0 x0 o+ B1 Y% ]3 \
1 D. W5 u. {- z\" F& V4 R2 s
要求误差0.0050002 w( n/ ^3 o# {5 W1 y, v
$ a' |# Y2 g/ T0 h0 m* t
输出矩阵为：
: _/ r+ G u1 M2 `* o
6 S8 [: m& t\" `, w( l4 ]+ P5 O& C* r; o
data_out =
: ^: v( m$ {- Q+ X, ]
* H8 s' i- F: b6 H2 G; f7 E. A. F
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
. X. ]: N, l: b+ d
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
1 b( R* {& x+ `\" k
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
\" o* O2 }! S\" d3 s3 E; c0 |6 Y3 g
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
( n6 _5 T6 k9 l- @+ T
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
& P5 L: L B6 h9 |
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000003 u- e; E+ ?! o
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
+ Y+ O, M# S* j8 f9 | \
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000, Q: b9 d) [( e3 d! Z
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
. }) }\" p# I) h+ T9 R
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
& z0 P5 S7 k& H) v; S
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
& q5 |9 R0 Y3 g* N
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000: r$ m, e8 j0 F2 d* u7 }2 c8 y
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
\" H) Z& I' }+ Q t
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
( k\" \6 m9 i+ N# o$ I
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
6 R) r. o5 f! x' v6 i
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890634 M1 ^8 e' \) a! P4 {
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
' h3 s$ }. h- X1 V5 G+ j. v) o( k
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972661 G. @1 Y3 O3 o! Q( n4 v6 p
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633' g. P8 z9 f6 g& [/ X5 V
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316 Q' y; _ s T3 E2 b
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158% w# H: ?, }7 z8 Z\" A
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579* u# T7 C( X5 X1 Q- Q* o* N\" B* _, k
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
# R! O+ L\" L\" _8 E/ i& j& M$ b3 u% H
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
/ g$ @\" E _\" k. b$ E' T0 E
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.0000000298023229 o3 T\" q& O, }. C9 `. c
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161, k `# J0 ?; l! H) q* K. @2 w
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
& l. ?+ x4 F9 E/ a* S4 }* K
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
0 U/ [3 n. F g
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645) D# P# r! i4 U4 J
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
* j- p$ Y/ g/ |9 t, L( c
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
2 j! Y\" d5 V3 E0 [/ E\" L, ^
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831& C\" E; e! r' B7 u- }2 H1 ~
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415- z7 ^6 r% l. T$ j+ o
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582082 u+ P. k- u3 Y4 A0 K- w
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
$ P. K i4 M& }6 V# a) T6 E4 {
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552\" ~9 a% ` B# ~! Q# R7 r8 v0 {
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276# J1 q }' U4 ?4 n' ?
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036382 Y0 V# w6 e( e' h. q+ _
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
9 {; ^% N+ |/ W$ L# ~+ z
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
) W8 z* P \9 ?2 Q. u8 |2 u1 Z
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455' W8 [# ^- G! V6 Q/ Y8 D, C
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
. P, f( \; K$ d$ ~
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
+ _3 c# N: D1 \% w, H9 x/ t
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
* _) @\" y0 H* y0 g+ h. i
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
1 n7 I# j: V% D1 U
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014( i6 P& O\" W* I\" f* m
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007$ v' |- Y, ?! }, }* v- n. d
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000044 k' ?( C2 D' ?, F$ h
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.0000000000000025 A. D% n5 y I* Y7 \% E# Y$ ^\" N& L
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
+ A& @: Y) D( i' r) [2 T
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000