[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
) S. \% @# V9 J, W% F8 {
% n=input('请输入迭代次数：');
5 C( R$ L3 s) o0 U# Y
% qujian=input('请输入初始区间：');
3 _; z\" w% U7 g4 G I
n=100;
\" C0 H$ n7 ~0 H4 [/ g, k$ ]( j3 B
wucha=0.005;
+ o {+ y\" _& X1 _6 u# G2 I1 I+ o0 g
qujian=[0 1];
! P1 c0 U5 m1 C. H1 k& r& ~
a(1)=qujian(1);
$ B) R# T7 v. r9 w3 J. L
b(1)=qujian(2); : C) w, p7 C9 q2 T* m
a0=a(1);
' [ X4 U$ a* z! I
b0=b(1);
; s: e1 q y' s0 w: V# T t
x=qujian;
8 g5 T: C! B' ~* i
y=exp(x)+10*x-2;) j8 P- q0 D+ F$ d# f) p1 J
y1=y(1); %小于0
3 l4 V# L) t& _0 U+ I7 k0 _
y2=y(2); %大于0
; v. i ~5 ]0 a
for i=1:n %总迭代次数
/ G2 }1 l% \9 |: L
c(i)=(a+b)/2;
$ ] G5 K( x4 U O% b
f(i)=exp(c(i))+10*(c(i))-2;5 j( l\" D- f4 R- w: n: N: l% n1 R
kesai_k(i)=(b-a)/2;
3 z8 V. I, x5 ^
if f(i)>02 q; {( z; {! O2 t4 ]+ x; C3 C
b=c(i);
; {- C2 K4 E3 b4 o t
b1(i)=c(i);
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a1(i)=a;
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elseif f(i)<0
% z; \3 O\" K) F0 s- H8 \+ ]
a=c(i);/ A# m! o8 S3 H8 b7 E+ S
a1(i)=c(i);) G% C' L4 Q/ L7 A8 j
b1(i)=b;
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elseif f(i)==0||kesai_k(i)<=wucha( O9 T* k* D\" ]\" w' l- k
disp('精确值解为：');
B/ h, }% @8 g! ^8 J
disp(c(i));! [4 W3 w: a& n
break;3 C! u+ @) y& {. R: G
end
1 x, x3 v, x3 w: b R; P
end
; `% }/ m2 W% l5 Z+ z% R
disp('迭代次数：');
. f4 x, S) a- |1 P, [4 n\" O
fprintf('%d次\n\n',n);
+ z* _8 Z, o6 M, x$ T
fprintf('要求误差%f\n\n',wucha);: w' X1 \. c: K
disp('输出矩阵为：');+ g\" ?0 ]; v- c7 d+ h# [
A=[a0 a1]';
) e: |4 r8 O\" m% Z; m+ Z, K
B=[b0 b1]';5 g! I- T- p+ @. `. |
format long, [6 y( {0 X\" ?' ]8 s3 h
data_out=[A B c' f' kesai_k']
7 e4 L! c; T$ p% G- z+ l$ 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：+ G: I7 X2 b5 q$ w\" w
0.0905
0 F0 W h$ e) g# S' b& J6 o& r! t
% Z+ L l# A, ?- j* I, y# X
迭代次数：
- ~6 l$ ^2 E8 |3 R3 ^# }8 o5 |
100次\" a+ E: P X6 M9 f$ V0 p
& m0 ?- y0 ?* I5 p' m0 Q
要求误差0.005000
+ }/ ]0 }9 f3 ~: d- F0 Y
0 g, R; \0 R& j! b
输出矩阵为：
8 M\" c4 h4 J, _
6 v1 X% A/ I. J& G8 `
data_out =
q+ q. {( c U Q* P
a5 f0 J& ~: L& y( }3 P) X1 P
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
& P! k0 i8 _2 B; x2 l3 @
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
9 v) W2 E+ g8 X' r\" F* X
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000# `1 Y+ j; J' p7 \1 C5 x
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000$ ~& p. @& P, w# r
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000: \' q, J1 C2 L6 F4 ]9 Q
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000! w; }2 x! c2 S# s- V
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
5 x! G( s0 x3 }3 f( [
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.0039062500000005 G# r6 J3 ] P
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
7 J5 e5 Y\" K' X# @
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
; @) I \5 H! x\" g. N) Z) W/ t
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000% M, l& Z) [/ e( |4 f/ W
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
8 P0 r7 g: }& P$ Q8 Z
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500( }1 X. _, P( ]0 a
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250' g# g- c( G0 i9 Z) o) R
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
/ l- ^+ |: v& H8 k
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
4 t$ A# ]$ r0 g( X\" s# V3 t
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531 L% `! ]* t8 \+ f3 @2 N/ E
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
4 \' n+ Z. {2 i4 {9 g
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
z6 |# p& v1 C0 h/ C4 p8 {8 e; A& x
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316- e& Y4 _# q- g; l: b9 K
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
$ ]5 ?! a4 o6 i8 }# R$ D
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
& S\" V$ N\" V: V
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290+ G8 P# m+ p3 H% Y( I
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645\" y* U) k U1 j! {$ b8 [
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322\" Z8 ~* A: l* D2 S9 n! s
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
, `# N! m# n1 @4 y1 `' q. A
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
+ {9 U# a5 \+ N8 X$ S/ a! r; e
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
% d+ `5 g( N' f' [6 m\" S
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
4 T8 M6 O2 F' L2 `& k
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323! g0 L' e+ [: Q% B( h2 _) s
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
# \* ~+ w% P/ X4 Q N* u2 H& e
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
( u3 p& _( }# `5 L7 y2 T* u# L8 t+ z+ S
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
- v+ B |! |# p
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208; m! @( i, R* C2 Y4 S6 ^3 @' \
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
0 k# w1 S& W$ \
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552. _3 x' s4 Q9 Y
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
& p# T: Q* j7 s4 P( g- e3 p% Y
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
: u, M8 B/ N+ e\" e( N. K
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018194 {) T) h7 S: V1 s6 E; x% n
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909+ {% V, G, m\" G) r
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.0000000000004551 R, ?/ I+ j/ q# i, @3 C6 }
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
* z) ?& W, ]. k+ ?' J6 Q- b
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
4 k9 |' v& i) C\" A0 R' {! C
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
$ Q1 S# |! f( K/ s
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
) Q& l$ o+ B# P3 s
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000140 ]3 `1 m& d* D& f3 ]3 Z
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
% k: f# U\" j! F: m. l0 F# F
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000044 \+ p- Z: r' u( ^
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
/ E% K0 V# P; p: b
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000018 y% K2 F1 S! \' B8 F! C5 [
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000