[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;close9 a0 T3 z& X5 c\" G, }1 }5 L$ N
% n=input('请输入迭代次数：');7 Q4 f8 y+ P9 C4 C5 {' R
% qujian=input('请输入初始区间：');
% \3 k: P0 }- ~4 H7 }9 P2 t
n=100;; S/ x* p3 D& K# O
wucha=0.005;
' [2 w0 B5 F5 P\" m$ z/ H
qujian=[0 1];
# I* x0 w. d( _6 A\" V% D( h5 s; s4 D
a(1)=qujian(1);
& t) \$ T\" o; s
b(1)=qujian(2);
# x; Z) X# ?8 V' s t0 O
a0=a(1);
& J# d\" F. F) V4 a; |9 M0 V8 g
b0=b(1);
. |1 ^; e8 F ~! r' f3 n/ f
x=qujian;# e' u7 @! B1 @9 S
y=exp(x)+10*x-2;
6 h) B, _5 B- j6 i+ G: f) r' c
y1=y(1); %小于0' ?3 U$ y$ g3 y% r; h! ^' Y, F
y2=y(2); %大于0. E6 K1 ^% G/ F! X& W2 _: A- V3 ?
for i=1:n %总迭代次数
3 M0 k! f/ Y& ?# _! }
c(i)=(a+b)/2;7 i# G* W3 t: E* ]# @
f(i)=exp(c(i))+10*(c(i))-2;
6 H; T, e- s2 z8 y4 S K
kesai_k(i)=(b-a)/2;
# K' f# E- f0 d* p% t\" t
if f(i)>0: k, l: @ }8 }# A- |) k
b=c(i);
9 e$ u8 ^% X- f
b1(i)=c(i);$ `' M2 ?, E\" F- P' X9 P+ B+ k
a1(i)=a; A, v& {+ W: D' |7 b+ J4 ]. S: o( o
elseif f(i)<0
\" K2 y0 I% t' G3 M) E4 c+ m$ h% ^: ]
a=c(i);) ]5 H8 E7 S1 ?/ q9 ^
a1(i)=c(i);
: H4 q) I/ ]4 W- Q4 p4 X- d# _4 v2 B
b1(i)=b;
3 Z( _2 Q* ?0 g1 Y+ |, O! l
elseif f(i)==0||kesai_k(i)<=wucha
$ A {5 B\" p\" ^: Z* q2 D4 l o
disp('精确值解为：');7 ]8 v: l7 R9 D% G
disp(c(i));5 F, L+ I1 Y! m\" g
break;# V& N$ p2 V6 a* e& H
end
3 E9 b9 L; [# }$ `* \' l; E
end3 D5 L% n4 J$ ?6 @. r' s1 a2 b+ u
disp('迭代次数：');
; }( c! _5 }4 e4 x; e
fprintf('%d次\n\n',n);- P- }# Z( A\" L6 s: r* d4 w
fprintf('要求误差%f\n\n',wucha);
/ `) x/ @+ a& R6 e7 O: ~3 {# {' D7 n, r
disp('输出矩阵为：');
6 j) U5 r1 r1 ?' Y( U
A=[a0 a1]';\" k& X- Q& F9 Y0 t& y
B=[b0 b1]';
3 ^) \7 R+ N3 E1 j
format long, B$ G' B) P W6 W. s
data_out=[A B c' f' kesai_k']
5 Y6 E, N8 W z
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：( W2 ?4 C4 ?; p% O1 C$ l
0.0905
* ~; m, d3 p1 z
: O# W\" a Q, Y5 h) H) q! g# S
迭代次数：1 X* j$ l9 h0 V: k$ J1 X# i
100次
0 C0 V9 j# ]$ Q; a; M+ Z
6 y1 I4 g1 Y# ]* {. n
要求误差0.0050005 n1 [3 }. I8 O\" D, b7 f) C
1 W+ m: Z6 q( w0 S
输出矩阵为：. H2 r\" a! Y9 ~9 X5 D, ^
7 N5 P1 T; E5 d
data_out =5 p, ~' F( l0 s: X/ S
; s0 I! @; \, a+ T\" c6 g% l
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000. \6 W2 f! `* b2 H
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000) E( l8 o: k3 H4 f+ V
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
4 ]( m+ E! D& d. w- [
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000, q3 y1 J* P9 Z6 p\" N# x
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000& ]% H% f* y# P
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
& p0 E# ]) e; p, F3 ]: r2 u# W0 G
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000/ K! A$ c$ H7 o6 \7 c8 \
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
7 Y& u- k2 h0 H V5 ~0 l1 T! o
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
3 n& G1 H8 g7 P3 R
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.0009765625000003 H. A, n9 R\" v7 l; F
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
/ y& x7 d+ Z/ x) a7 L, k
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000: R- i5 e# k: i0 {% d
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
6 {% V6 i' T3 Y& j+ ?4 ]2 b9 {
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250# \' Y0 j) E/ S
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781259 Y# V; ^, J' I3 g
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
7 @% D% D' |! z0 e, d
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
$ r$ s r* p( K
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
4 k5 D G7 C& E6 Z9 D
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
; L: h* Z! Z1 v* V3 S+ o/ K4 F' S
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
& r4 }4 k1 g& q+ Q0 O1 W. P. U
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.0000004768371584 l9 s! [ g4 t, y7 K; `
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185794 e& y& N: w9 y4 x1 k: V6 [
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290$ a: V2 D$ c9 [( ]) a: I8 F
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645; G5 @$ a' V) f0 k$ K7 ]/ N
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.0000000298023229 `( ^, k( ?\" m' e3 S m3 P
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
8 N/ @! {% T' H4 B* U$ q, B* u
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
1 _( f# q0 O, f+ [. l# f
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290( {. l# j4 l- z$ v+ q
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645+ G( W* B- y% o. n- ] J
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323' L; a7 X+ O; n: n. \6 A
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.0000000004656612 |/ T5 I) _4 ] i: R' Q
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328317 n9 l9 [6 ^ S5 Y$ a
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164151 m: m4 ^- M- r V) P8 I! u2 U
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208' K7 c' P+ z* F, E+ `* a
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291040 ?8 X, l/ F V$ e4 I
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145529 D\" Q4 f( \5 C# l: [* J\" I
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
+ a7 x& X/ e7 ^) i
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638/ f1 H. M: V: v) ]6 h+ Q! z
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819- G& H a/ k# ?) n3 I\" b3 ~
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
5 ]7 M+ L# n @6 Z( _& E
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
+ I( m! G* }8 t4 y0 f+ z
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
$ v+ H5 S9 o- r: \* J
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
8 P+ x# ^, |! {( S; x9 ~\" V
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.0000000000000572 S& t3 L1 r- P2 M* e/ W0 w\" `) Y0 h
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028! w c8 L& ~! S, m$ b
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
% n4 R1 P: h( H9 P Y
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
& [; G1 w6 o( P
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004- ]; c6 {: s6 k7 P3 ~, u
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002& F0 T7 B, s9 G+ c
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001/ ^) a5 }# {% i0 t6 `\" ~* h
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000