[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
. y& D; t# C* \% @. v, n
% n=input('请输入迭代次数：');
8 s+ q* o/ a E
% qujian=input('请输入初始区间：');- S9 \7 v* o( |5 {, O
n=100;
6 y. c: x% T J3 d$ O2 n% i' m; [7 Z
wucha=0.005;
+ Z4 z2 R5 n. P4 b9 n! d\" q) E
qujian=[0 1];
6 x, U. i! n; u8 {# j
a(1)=qujian(1);2 v. L- s5 G) _. [5 ]
b(1)=qujian(2);
. Z& ?* G% \3 J B; F6 A$ V
a0=a(1);
% a3 _) K2 R( M/ a7 j( y% O
b0=b(1);
1 Y T4 ^: h8 ?( V1 ]
x=qujian;
/ U% \! [* `; z1 D3 C
y=exp(x)+10*x-2;: W m+ l, Q( ~$ ^. m# r
y1=y(1); %小于00 ~- N1 x! X* Y* y
y2=y(2); %大于04 {+ W$ {' c0 c4 d7 V4 Y
for i=1:n %总迭代次数+ @ }2 C3 N1 p! X& I& s6 }
c(i)=(a+b)/2;# w/ _4 h# n) J X# W! a2 t8 ?
f(i)=exp(c(i))+10*(c(i))-2;
7 T3 S; e6 N0 r
kesai_k(i)=(b-a)/2;
- s1 w7 w: K9 W\" Q9 U. J
if f(i)>0
2 ^5 s* a, e$ v$ G
b=c(i);$ _% C+ `2 m! p6 V# }
b1(i)=c(i);
% s ^0 _$ C: K: c
a1(i)=a;2 V* F1 x/ M1 J3 s' d
elseif f(i)<07 f# ^: @ O$ X7 r7 D7 w& h3 s5 n
a=c(i);5 {) u6 s9 e; c- ~
a1(i)=c(i);/ b8 \% e* \. w' D$ d4 n4 K
b1(i)=b;
6 G, u& d1 H9 ~/ K\" n7 o
elseif f(i)==0||kesai_k(i)<=wucha* [- t0 B g1 a9 v6 {* s! W4 e
disp('精确值解为：');( G% R J/ }- [5 j% ~4 Y# k
disp(c(i));
0 [& K. d) u6 q- v
break;. @8 Y- d2 V. e0 c5 ^+ i! X; i
end, k, e7 s& D* M- Z7 Z
end) [. i* Q- R. O1 R9 ~
disp('迭代次数：');
+ ~( w1 S6 |/ `& g
fprintf('%d次\n\n',n);
# R) r, g* U2 P2 c& H- h
fprintf('要求误差%f\n\n',wucha);
; C% j0 ^0 z8 Y3 Y* T3 e3 K
disp('输出矩阵为：');5 i M R* P' N\" P, V
A=[a0 a1]';
% U* _\" J# c$ x/ x! V/ w
B=[b0 b1]';
9 v6 i, `& [. a. I4 ~1 s* m+ @
format long' c% [2 K/ W! V; F5 @
data_out=[A B c' f' kesai_k']
' x* W1 A p, z4 I& x1 @$ W1 @
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' i) w- c$ I. _1 R
0.0905
, x8 x$ s: X7 A, r5 e, c O
7 \# K1 H& ^5 o+ `4 c. t* K2 c
迭代次数：% O/ F3 y! b( J' j1 [
100次$ t$ m2 r7 ^' [& g\" a\" c
/ K3 A3 Z, k0 O
要求误差0.005000, U* `2 a% {\" b0 F0 K
+ x$ J5 _$ j: j\" T. l
输出矩阵为：$ C, n\" I S2 t7 }: Z( f6 ?
% I/ t: Z4 T- x p7 O* z! C
data_out =
V$ x. k$ R\" h* W1 I8 X$ G, z* n
4 j, H$ A$ O9 W c% c L' G; s0 h
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
; _; C- G1 N) }( f T$ e7 f
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000002 J6 g4 P; u: U+ C! m- n B5 P
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
9 \% U) m+ F. ~0 m. x, m
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
0 u3 e. {2 J7 q0 Y. p/ u5 n- D
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
: s; \# c+ T3 t
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000& N( p5 x5 ~0 @2 y
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
- v1 K! x) F9 X2 t3 t
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
5 _! Q) {! I5 B8 @3 t8 B/ \4 |
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
5 Y/ [\" \6 z2 Z+ b/ T
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000) c5 X% m8 R5 q6 i$ Y& [& L
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000. M6 _: b! w: [% O
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000' j* ^9 t0 w0 v& s
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500! P/ ^& I+ K& k( r/ A. i! |
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
+ I. k4 z, z9 ~+ h( p
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125& ?0 r9 n+ x3 _
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063$ v$ ^# N2 S5 ?0 I- o
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531; Z. ^! @\" |0 f% c. E
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972669 D% w! B7 _* ]4 i8 U$ @& g6 s
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
# q' X# x3 M\" G6 I
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316. i9 f: L3 J3 k# R' n$ D
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
& G* k5 o( W2 K. G/ d- C
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579
& p& y$ `2 f( U: B
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.0000001192092908 }& h# t2 X) h- G. b\" T; D
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645& R. P( C! F5 p# V& T: R
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322\" q: c4 P4 G% j. ?
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161( ^. F, J; Q& [# `
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581& u2 q% f, v* o8 b$ Q8 `' U1 E
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
1 S0 ?$ c; j U) x
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645$ _) }4 E$ I' E' O
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
5 X1 ]. ?+ d* p
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
0 y3 R G9 I\" A' e6 [) e
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
- \, E/ {& D6 m0 y6 r
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164159 O7 F# |4 X. B) V
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582087 R! \1 Q1 M8 @1 [. F
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291045 v0 `. }% b- m, a* E\" B9 C6 ~
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
5 @* i# c8 f, k2 f2 M6 e
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
, o+ E/ D$ U; }. K9 y\" V |$ Z1 Y
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
+ s! V0 E1 L) [) x$ S9 T8 |
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819% Y/ Y' j7 d# w F2 C1 y9 U7 x! W
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009097 A1 H. [& _& c) l9 J
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455$ y) q# u& v2 g
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227! a7 @: \, T# J2 E* r\" r
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114; | t' M4 @+ X2 d3 R( B
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057; Z9 o\" m& \6 t' b
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
9 O( C `6 [3 E7 e+ O5 F3 t
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
) n/ ~& ?( A& N( \% O
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
7 f2 _, X& e7 R* W! D+ i/ k
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000048 e; a2 | \1 [! Y
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
+ y\" f\" s5 a4 T6 K9 g, b* {
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001. G' x. c0 u+ W* m3 Y6 j( F
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000