[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, _2 b+ Y; q/ j& i$ O
% n=input('请输入迭代次数：');, d& c& u) y: p- s y
% qujian=input('请输入初始区间：');$ Q% A6 C/ {- a ^) J9 E
n=100;' w$ q. y6 k4 m% `) C; r9 T5 w. i9 K
wucha=0.005;% d6 {& I* W( K2 M5 N. T
qujian=[0 1];
8 c$ I0 m- K0 b% t% x. i
a(1)=qujian(1);
$ g* z) `7 K' O, S* d7 g# M3 e/ ~
b(1)=qujian(2); + J: M) j0 b# w& q0 Y8 A' v5 x9 \5 r
a0=a(1);# W' @\" y# l0 v# p, i! H
b0=b(1);8 V3 O4 ~4 U5 {6 L2 h5 J( L' A
x=qujian;
y=exp(x)+10*x-2;7 \' H7 L8 a6 n+ |0 D\" ~
y1=y(1); %小于0
3 a: V& @ W9 U& r7 ~* @
y2=y(2); %大于0, J$ q: k6 z, A {% s6 z\" ~
for i=1:n %总迭代次数
B% m* R' o5 z& W
c(i)=(a+b)/2;( S! [# q) p5 m, R& |
f(i)=exp(c(i))+10*(c(i))-2;
' i x, Y* T+ t& x4 T( i% z
kesai_k(i)=(b-a)/2;4 R* D1 b% K4 [& s1 L\" F
if f(i)>05 m: L0 ] s4 Q9 ^\" ?\" E. z
b=c(i);) i' _5 e* v* c+ r
b1(i)=c(i);
+ v1 \/ X% |. ?- d/ S- T
a1(i)=a;
* e3 i; ~5 `* W\" n- l3 |
elseif f(i)<0
; |/ S2 A& _: E+ A
a=c(i);2 [- D) d$ q* R\" D. X1 q\" X; x
a1(i)=c(i);% F0 @: p$ ]# Z8 W0 r
b1(i)=b;) ]\" P y7 t6 t
elseif f(i)==0||kesai_k(i)<=wucha/ n. i9 G A\" m( T+ y6 Y. J- w
disp('精确值解为：');
4 I) m; y! L7 M0 D3 L. j% @9 c2 \
disp(c(i));% J. i+ k' u( ?. h( v: l; j
break;
' _; q6 i) y4 c* r- }2 D
end
9 c# j0 i5 a% U$ _/ ?
end
, T0 @) g/ h2 S% ~& A1 ~) V
disp('迭代次数：');% B- X2 o, B\" z4 Z
fprintf('%d次\n\n',n);
% y: `2 k7 _* B$ ~2 `
fprintf('要求误差%f\n\n',wucha);5 {4 a) X L( J( D
disp('输出矩阵为：');\" z3 v. E( P. d
A=[a0 a1]';\" ^9 k5 H+ E) V5 S' p, ]* d
B=[b0 b1]';
/ |# @6 K0 K/ o0 P: q+ m
format long
0 u/ q& X/ ?# w& ~* n) q
data_out=[A B c' f' kesai_k']
' K& b0 e! D6 p5 L! T' F. d
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：
4 l/ G7 W7 E, @3 v
0.0905
; {3 {/ W1 n! \2 D* e+ _4 u q
- G. V% G4 w; `' s6 q
迭代次数：* V5 Q9 q% K. P) H7 _6 K4 G
100次
5 c: E. {\" \5 H! q6 {
9 k' V5 Y6 o! o
要求误差0.0050004 N; _ C9 h; r D6 P# P. I4 Z/ {6 |
; t8 M/ a( L* f
输出矩阵为：' O: p- G% ?( H+ d' g( G
8 p! i: w\" I7 N, Q+ W% V6 V) b
data_out =
9 c7 Y% r) ]6 S% F( I( R6 j, ^
1 t; ]\" f+ P% f. j: {. a. E1 ^1 \
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000& c a% Q7 M& y' b! A& }
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000009 i9 E6 j4 ]5 p2 f9 y9 t7 h# H
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
+ E& R: a' q9 i# F2 y$ n5 U% X' i
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
. w. t5 D& y5 o+ F) S* O' i
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000! j7 ] @8 o' \0 D- X+ j: L2 `
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
$ x) b- a- l8 S
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000\" y5 {2 C0 r$ A+ M
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.0039062500000007 R) K5 I& K$ t7 y
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.0019531250000000 X/ R5 d4 u0 ]
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
& B; V3 m* }* D8 L! {- _
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
$ G# }) D2 V; K. [4 n
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000/ w+ Z4 }; n9 Y\" G
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
5 [: v7 \1 k9 Q! y3 _( r1 X5 T
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
1 w8 S0 T# v# n! b2 Z+ j
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125* D1 {$ Z4 B ~! a7 T: O2 b8 H( G
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890634 H, @+ v9 `$ ~
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531+ T* U4 l( n0 h
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972662 l$ z7 s& j& i9 z0 F* |- E
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633( J( |& E' l+ L
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
1 ]% a9 i# X- l* X9 v, e* z0 \0 }
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158# n; i) d, w5 O4 b
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579+ D* u$ j$ ?7 v. L1 Y
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
1 p* f\" `\" ^' y* l
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.0000000596046453 ~7 o, N/ T- i' X$ g/ I: ~
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
; H8 @9 w4 q4 D\" B ^1 Q/ o
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.0000000149011619 M9 ~. R' u4 |* e. k _( M
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581: w0 ^9 ]9 t; O' d2 O& c
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290\" _! L. K\" ^0 O
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645- t4 \4 ]4 Q9 F5 G& I# J& r% @
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323 B. N* m) a7 {6 f: `
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661 u7 ]. Q6 s+ K: ?3 a2 ]
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
# h! q7 A7 o' Q8 \, J2 F1 ^+ w
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164152 Q/ J( u8 \ L# k# t( m
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
: F/ u, |# a; G: ~4 |9 K
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
$ y) z9 b- @! B7 o5 ?
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552+ D* n. {- L: [! r# K, K# w) f
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276; c* G+ x' V: D
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
+ ^. |2 {8 C0 R8 G6 v\" ?, P& K
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819, S3 T8 [. ^, u7 a
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
/ w! g3 o# B; |& W# T
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
) t- j/ s0 G) S$ a; p& _4 G Q7 m
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.0000000000002279 ]% @5 [4 ?* T3 {
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
' |1 |3 }3 j2 {: I* \
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
) c! r- |2 T1 x: K) f1 G5 y$ T
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
0 R f2 _9 L! r6 f
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
8 v7 I; a8 t' h& _
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
7 z: W$ S( U5 `\" G, O) T! n
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004' n; F4 c3 f3 r0 u! O8 V
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002& u\" I6 \ `5 _8 @4 q K! |
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000011 q% \' X\" t( x0 k% V7 o* V1 r
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000