[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;close7 R) d\" x0 B, d: ~! S
% n=input('请输入迭代次数：');, d6 N w1 @: M+ Z\" [
% qujian=input('请输入初始区间：');9 ]' _# s4 |1 V6 B' a5 d, R X0 i
n=100;* g* H3 I) d- D
wucha=0.005;
* ~) G$ d( Z1 b5 h
qujian=[0 1];8 ~$ u8 R5 N7 k6 k- ^! n. u; O
a(1)=qujian(1);0 s% d6 s) \4 D\" A6 `. c
b(1)=qujian(2); % ~* E* [! ?- K6 S
a0=a(1);8 n* X; S, k$ f0 A
b0=b(1);\" ]) x9 _' E @' P8 |: c: A/ w
x=qujian;
+ L) [( \! p5 W3 [5 u% i: p
y=exp(x)+10*x-2;
5 u- G7 {5 X7 g: y8 _$ y
y1=y(1); %小于0$ M: B/ F: V2 D' U# ]5 a
y2=y(2); %大于0
_6 l; \- C( d: o8 s$ u9 T; P
for i=1:n %总迭代次数
. {% D/ M( l7 f- v
c(i)=(a+b)/2;7 b' l\" V( i# v5 }7 ^7 m' H* r% H
f(i)=exp(c(i))+10*(c(i))-2;
5 u. m$ c$ x+ M% T# p9 c Q
kesai_k(i)=(b-a)/2;! u, q( T2 m2 N3 z( z
if f(i)>0
' S\" }3 I& s+ F9 y- y, Y
b=c(i);3 b! h5 h3 h% x3 g& j! B Z
b1(i)=c(i);3 b6 @1 S: A* r3 G
a1(i)=a;; V- ` K m$ M
elseif f(i)<0* l$ l* u) T2 Z' h i+ M ]
a=c(i);0 E, d! U/ R2 t0 S
a1(i)=c(i);\" @# M7 B- y5 k8 {9 D# O' u
b1(i)=b;7 U% }5 M6 I( ~7 F
elseif f(i)==0||kesai_k(i)<=wucha& ^: ? ~) G2 ~! S$ r& [
disp('精确值解为：');
6 Y2 F( m, b' V k- A E, K8 t
disp(c(i));# u: t8 w3 l! S4 I
break;
% u) M. x+ L, X' W2 \3 Z1 ?
end+ n5 ]# M7 t$ i) a8 V6 b
end8 V\" k, ?* }: o
disp('迭代次数：');
& `# T+ g0 O7 R0 A4 A0 _/ F\" ]
fprintf('%d次\n\n',n);\" y0 x# p# `2 R1 v
fprintf('要求误差%f\n\n',wucha);
N, D% _$ y! u
disp('输出矩阵为：');
W6 }/ u% ^; g! b
A=[a0 a1]';
- F) S/ c3 e7 z& _% j7 e6 {
B=[b0 b1]';
& {1 V( n) E v) L U% C* ]0 K
format long0 _& ~- I\" y4 h7 T
data_out=[A B c' f' kesai_k']+ P% k0 w; b+ W9 H( q7 j. J- j
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：
! U' I3 R6 q- |\" Z
0.0905
+ S3 s+ h. j- t) D
8 m/ r' F; k6 f
迭代次数：. K1 b9 a3 N, r( c
100次 n$ L. ~- U5 z# t& L
/ ]- Q7 c5 g; X9 q/ \
要求误差0.005000) U/ y& v. V; W* z- l
1 t8 F2 U6 _! \1 v# Q- y
输出矩阵为：
$ Q\" M4 w6 {* @3 G4 V
# ^! P* Z. [# V+ f9 K: ?: j) M( b7 D
data_out =
7 \8 S* v, t9 E( z. l2 H
' G: T& F$ E\" H7 @& ~, _
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
5 z8 M0 g' L+ f
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000- A/ |( s6 ]& L$ o$ v0 a; K2 Z
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
\" z& [- W, E0 j, n' n( W2 ]
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
* G; d4 Q# H+ ^3 P( @) r7 }2 s9 b
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
' i: b- h7 j q9 k! c
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
0 L. P- m6 {\" L7 m7 h x: I
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000000 q' G) M/ H* ~& p7 e6 z
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
2 o: W U5 P: R6 c* V; o2 j
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.0019531250000000 s& L3 n; t! p2 i
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
2 N/ |8 q+ s% Q) p, H\" |- s5 J
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
7 y- o) F2 D* N) r+ p S( Y
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000& N- @# m* J6 f4 K# V
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
0 Z2 f% g3 x' m2 K/ o
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
! n, h1 ^1 z6 |: q3 J+ k; h
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125' f: u G, j# U
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063( n/ y$ q7 q) k
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
% w! e; ~+ n- i1 D/ E6 y
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
' c. v\" J: _' D3 `
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633) b/ f. U# u3 n5 g$ F: {
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
5 r. r4 w1 S: }6 [
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
2 l5 |. q, z3 z. [; R
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185798 N* H: c, e8 W
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290' ~8 p) P8 I+ ]4 k5 l
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
2 ?% r4 b- K- K- ]
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322) Z0 x& b5 p/ A m$ E6 O8 |$ k
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
; T! B4 E; P5 Q: w: O4 d
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581( l$ k! U1 H* C9 n
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
, A\" ~6 O2 k4 t1 k
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
/ R0 z- @- \& m9 ?1 e* D
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323! S8 S5 e! l) F* Q. Y7 M
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661, j1 i$ q! `1 o+ E: d% {$ R. f _
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
7 k$ T+ \3 }* {% P0 V0 ?8 l4 u- c) w+ K
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
' S- u/ e' V6 r3 S; p
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
9 L! J& w) n! R% B) _: {
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
n! Q. |6 \4 {' z
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
* s0 M( G9 w: G( M, l% ^
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276: P$ r# O. O' X# w
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
J- B. B/ \' F2 Q
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819& S1 ~* N: ~$ j7 i
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
0 J\" }+ D/ f+ N/ M+ b- X0 v( P/ m
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
0 ~\" y0 v2 [, f4 {
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
# R u5 T% |0 o3 u\" A
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
) I\" f+ B% d3 u1 u2 B* x: v- P
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
2 m$ A r: b! y
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.0000000000000284 ]\" D( Y; a* O* N; k: m9 d1 T$ q
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000145 R1 C$ k7 _% _+ P% O& \9 Y: x/ P
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
1 c8 G* a, G# q. f1 R
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
9 ]- ?6 W' h- Y. i; B
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
5 ~, Y4 P- S1 P% f9 x
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
: v: r\" P3 }* x6 e# K9 m
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000