[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( \: J; n( Y9 f0 u\" ]0 e# m
% n=input('请输入迭代次数：');
; _. r0 V: Y! a$ Q4 I8 O; I
% qujian=input('请输入初始区间：');7 u! F# E7 {3 I
n=100;0 o2 a6 [7 `, m1 A4 o
wucha=0.005;5 ^6 D Y! E7 `+ ~- S
qujian=[0 1];
$ I- x5 \2 _! x$ O( B) @
a(1)=qujian(1);6 a- K; a: h7 ~/ J: f* M
b(1)=qujian(2);
% m\" a+ E! ^9 s$ {. ]
a0=a(1);
/ U) {! n: O( ?( \' b
b0=b(1);; z' E$ X: w, X0 \
x=qujian;
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y=exp(x)+10*x-2;, c8 u' ]$ e* ]; n' Y0 A
y1=y(1); %小于0
! M2 {* O! Z* t' d7 e, I2 F
y2=y(2); %大于0
$ R. b$ x6 I) V7 G\" X
for i=1:n %总迭代次数
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c(i)=(a+b)/2;
3 z* _; g7 f) i) Z: U3 J6 ?
f(i)=exp(c(i))+10*(c(i))-2;
1 |- y) o8 c1 s1 `
kesai_k(i)=(b-a)/2;
, B! E9 k0 t% k; r5 X, {7 F- h0 b
if f(i)>0
% o; I# l* Y! E8 L
b=c(i);$ g6 m9 h# q; z# `9 M
b1(i)=c(i);\" E\" I7 R ~5 s7 o- B# v
a1(i)=a;
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elseif f(i)<0' j6 W& f7 E. C' c
a=c(i);( Z4 u' ~ u; S A m
a1(i)=c(i);
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b1(i)=b;
$ V& U Z H J
elseif f(i)==0||kesai_k(i)<=wucha
* R7 J* d# H6 c
disp('精确值解为：');! Q; L0 T0 q1 l& ]2 e: |3 x
disp(c(i));
5 t: h4 A8 d7 `$ f5 S
break;
% Z% e% }6 R, k4 o* ]
end
. u4 O1 \; t. C
end4 J+ \ _* S/ P& p# _: {9 L
disp('迭代次数：');
% y! a: `+ z F4 o9 q. H
fprintf('%d次\n\n',n);1 e! r/ r\" J$ l5 ~3 q
fprintf('要求误差%f\n\n',wucha);
0 X( L8 n) P- ^. X P
disp('输出矩阵为：');7 x; M& N* p( `, n5 X' P; G
A=[a0 a1]';
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B=[b0 b1]';' p! O0 Y* n. U! k3 A
format long) x( p5 C, ]\" C\" ?: P% l' e. q
data_out=[A B c' f' kesai_k']
* `' A5 q( Z8 c
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：
5 W+ s. o% ^4 \, U [* i
0.09051 Q! ^ O; n# E0 p/ P w D
9 k, J4 W* G4 U/ M' U$ G
迭代次数：: M% z( k+ m' x t3 i
100次
8 D0 [: W' Z7 C. q8 i
# J\" G1 c5 g: L) A* [- e6 ]
要求误差0.005000
/ G$ y Z* R6 R! j+ f- \0 O) [
' D\" V' s8 K9 o
输出矩阵为：
( N+ ], u& x, E- W* k2 j' u
# Y# L; J4 V+ p4 f! E U/ W1 x
data_out =
6 `- I5 W) u% t7 f4 Y8 l2 o8 X
/ ~) [' q1 c* _
0 1.000000000000000 0.500000000000000 4.648721270700128 0.5000000000000002 z- [( Q4 B+ b. D; v
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
& h E. c! K5 c* L
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000' i2 `) Y! M7 j0 `3 ~8 H\" f7 [! h
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
8 O f8 T1 f1 _, m
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
& U; m4 D3 @% @! E6 L: e7 M1 B& ]1 B
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
0 v8 c9 a* x+ N- P
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000004 \/ r* h9 ^$ Q' j\" U5 U
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.0039062500000009 r M\" q\" {6 r N9 e
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.0019531250000004 `% I6 t6 P3 N. B& `
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
. |) @1 ^7 @\" u( V% ^( j
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
2 _! W1 I5 v# z9 a- d6 Q; u) a
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000& _% B3 ~# R: G7 S
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500\" b6 \3 K% p1 f$ L, x) i3 }
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
) K+ l4 l1 h, _: }( U% r1 A
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125 C/ C\" \1 I7 N+ @
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063 g1 A7 P9 {\" g* q
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531: i4 }0 b8 X t1 G
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
/ ]! O+ l9 B0 {; o. v' D& K( Q/ q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.0000019073486331 G* w& j% P\" o9 m
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
4 E) V2 @% c; l
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
1 Z: V# Y2 W& W3 p% s# ?\" R- h9 w
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
/ n4 f. N) o3 U; \( A
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
( Z$ g; Q! \. i
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645) G3 K& r\" Y2 E* k9 [
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
. I+ j* K6 N2 ^( s5 ~, {; W
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
0 U0 A5 n6 y' u& S3 T2 G L; _3 l
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
# ~$ p8 f# ?' _+ O# H& F
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
5 j Z\" Y/ t$ ?* W7 _3 }
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
0 k9 t- y. f# p# s5 c B- H
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
+ U. ~ r4 [: O1 `+ y# F8 v
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
- s# J2 A3 g& M# U( b y) q4 c' E3 R
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831. T4 c% f$ z2 A, S6 |! h
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
( D\" d+ U5 L! P; k9 O* Y+ }
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
, ~. p$ Q% |' ?3 d* W$ d6 J
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104) I9 \# ~0 j% ~
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145526 y7 a\" d8 L, p* T- [% [4 r2 U
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
; {# v% t: L/ c\" v9 T- `- M
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
- m, Y0 @6 C$ V7 A
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
2 U# Z. H2 ]) ~2 P1 i
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
9 K& P+ f4 N5 {5 z3 e
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
: o3 f: J# a/ k4 }7 R; o
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
x' s9 P( G/ ~5 @4 `/ c
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114 ~, g! u; `\" o5 {8 w
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
9 [% _% t8 a z5 Q; u
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
; j1 p0 } E( D) B, A, t# p6 C
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
3 K Q4 |% u+ G' P' @! b2 z6 w
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000079 W6 U; q6 V; n\" o9 S3 {
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004' M& f# p( ^3 s# L5 U6 h
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
6 I5 Q5 u; m# H5 O
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
2 `7 t6 S9 _. q
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000