[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; o# Y' D8 p& Z) V0 F
% n=input('请输入迭代次数：');! l\" A4 r2 S1 [! U5 V, r4 ]) A1 q
% qujian=input('请输入初始区间：');1 Q p% _$ i- M\" E- x* S) [( y ^+ R
n=100; O& s8 I9 ^5 ?! N( u: \ g; L
wucha=0.005;
1 S; v$ V' y) i s- S\" g
qujian=[0 1];
6 q- A. c k1 H2 r
a(1)=qujian(1);: i2 O/ e( R! X
b(1)=qujian(2);
7 ]2 I( J\" r' o1 V% x }
a0=a(1);
! m/ V0 o1 Y# r. i\" @! K% H
b0=b(1);
% U# a( U. s5 W+ L# |- ^) P& V
x=qujian;& j/ }' u9 L! t\" O* L& m( D5 w* P
y=exp(x)+10*x-2;; d3 j+ K0 y1 h2 K
y1=y(1); %小于03 Q# p* Q- S' m4 A
y2=y(2); %大于0/ u7 e! f8 y, u& C# M
for i=1:n %总迭代次数
9 B5 O; [4 S; ^3 l3 e$ o9 R
c(i)=(a+b)/2;1 a8 e8 a2 V# q# T\" X8 W: r
f(i)=exp(c(i))+10*(c(i))-2;
: t. H; g) G\" V& i
kesai_k(i)=(b-a)/2;
% t: \2 ]% |! [5 [
if f(i)>0; s( j( O$ q# X3 w! s
b=c(i);
* k0 B/ u- T) G6 {- e0 I
b1(i)=c(i);2 k0 P$ J; \# L6 Z) u! T\" Q
a1(i)=a;
8 c8 ?& m/ v* z, R) j
elseif f(i)<04 X+ l; h- |0 Q P# G
a=c(i);6 Z& T& d; X' A( Q
a1(i)=c(i);
! e4 n) S! ]& W5 K
b1(i)=b;, O- L) ] F2 A U\" @
elseif f(i)==0||kesai_k(i)<=wucha
% t% n- J1 I7 r# y: q
disp('精确值解为：');
& U4 V/ i3 p' x$ h% a. W
disp(c(i));' d! F8 @) e# a$ e8 Y: A
break;/ D4 ^! l3 g# f( `! ^5 ?8 K
end
5 V/ h3 s7 D\" }' F8 l
end2 S' X# C# t% Q9 t' |) D
disp('迭代次数：');; D) _ e; J: B6 n\" o7 Y
fprintf('%d次\n\n',n);0 M- S5 E7 g7 R3 l/ U& M
fprintf('要求误差%f\n\n',wucha);
* `5 |4 }* W. j5 S6 Y' }6 x
disp('输出矩阵为：');) c7 g- a2 f$ r1 H9 J8 k/ k
A=[a0 a1]';! c0 a- O# [: |1 o! i: p6 o
B=[b0 b1]';9 v* F1 N4 |8 t5 V0 S
format long0 T, Y# E\" f$ [) G0 `
data_out=[A B c' f' kesai_k']/ Q\" p$ k' S0 R6 s. J\" z' O
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：8 e9 b; B6 p, }, @2 E
0.0905
) p1 y, }% _$ p- T* n7 ]- h. F7 X
# E\" i' e) n! n
迭代次数：, Z0 s\" d9 a& ~ j) f( c0 T
100次\" ?( ]\" x/ q: |+ g5 j
/ f' w% \$ J& A! X g1 y
要求误差0.005000& ]' K+ h* R+ |7 y8 n2 d
- d7 E8 p- i' D8 G; Y\" c
输出矩阵为：
8 z; a7 L, Y) X( x c; }
& j; D# X4 \1 q7 a! }$ ?9 n# c6 v
data_out =
! T$ r$ k( U, G, h+ t
9 `\" h\" U! C1 \! w\" T7 I
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000/ d\" M( o; Q7 S* m
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000( a# X' {+ j7 _! j* H, D4 s
0 0.250000000000000 0.125000000000000 0.383148453066826 0.1250000000000002 A4 H+ i: S+ Y& W3 ]& X2 R
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
1 p f; r\" ~: ^9 Y8 D8 c6 r n
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
4 n$ o7 d\" d9 M. w! {
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
+ ^! V% ]3 ?, w- k: m1 `% V
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
K0 b/ U. q# P% H/ A) {) W
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
0 m5 x! ?2 @3 _, A+ p# z
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
1 N( G) B2 h3 v b! W# {/ |: K
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
1 f' K; c) R- y9 m8 ^* A
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000' c8 G: j& e H/ b8 d) D) Z1 }
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
! v+ L$ P\" h9 v. C' G* _( N
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
: M& o q4 ^ x' d8 r7 H1 b
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.0000610351562500 U7 V\" z/ A2 K0 v
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125* O! J8 s$ M$ f
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.0000152587890639 E @! t( M* R4 Y
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
A* b$ h\" }3 _# |$ h
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266+ T8 m% a u+ n) M5 {% G/ G# t; Q
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.0000019073486332 ]' `% s2 ~3 e i4 [
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316' @5 H5 R! i& N
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158+ I: r) c Y4 D' X
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.0000002384185798 ~, _3 M8 y# e+ Y9 ~7 \) G
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290) s( k5 N* v. m t# O) R2 y
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
- ^1 U6 D- T! J0 m/ ~% u. E: A) \ p
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322# b- v$ z3 Q5 |4 Q$ s+ C
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
/ a& b3 g: d3 }9 w, g. M4 M. P
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
' D! X$ U5 w+ L; o2 k9 ~\" Q3 [* y
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
% a\" l; L8 K; O& v/ _7 G: a
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
! F6 L# n; b5 M7 \# e# _
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
7 A% c6 P, P4 ]4 ^& t
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
8 _- g+ k) u3 Z4 k1 B% u
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
U. M! U0 l- W' f
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
\" I4 _: f/ D% A1 X2 j
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208/ N1 \/ K9 Q/ Z$ u; B1 _4 O
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
& F; u\" }# j4 _- a F
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
# R T$ W7 ]5 T g
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276* e( l$ m# U( S5 F/ t; }; a
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638; U; d/ J0 N\" F. t( n: E6 }, l
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
1 X; C, f# Y/ u% O
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009094 C' s- ?+ e& M8 g& P( Y2 b/ s' n
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
7 ?- b9 X/ I, h, q
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227% W. p\" T3 ]3 Q5 X- C5 o1 }8 |
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.0000000000001141 j, Y/ o k- z2 E3 H) Z' [
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
' W2 p# z6 m. N: d- n
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028% F2 F0 V# c( _
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
/ E2 H\" M8 J\" `\" O( y& d; W2 ^
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000077 }- m4 a! S9 X7 f
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000046 f8 K/ ^/ J* l' L$ I4 N7 ]
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
, Y1 ^2 x$ S0 m# ?/ Q% R( F
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
4 t# v! |\" n! h
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000