[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' c3 Y% A0 X\" h( g ~
% n=input('请输入迭代次数：');9 `/ W2 l5 f/ g% d f\" L0 P
% qujian=input('请输入初始区间：');
7 _9 {8 h$ `/ j8 r' @8 x2 B) F
n=100;
; [# j0 y& F b1 Q9 H
wucha=0.005;( ~3 P8 |7 V9 p* P6 E1 M
qujian=[0 1];
5 ^9 L; ~- @0 g5 p- b$ m) @
a(1)=qujian(1); K7 s4 I/ @# o
b(1)=qujian(2); . j/ @7 F# @- Q( o2 C
a0=a(1);. b- a) h\" D/ a7 }
b0=b(1);6 p2 X7 O) W w2 ^
x=qujian;
1 K# s9 J3 W; s2 Y
y=exp(x)+10*x-2;8 g7 \, [. i+ q! j) ^. @7 j
y1=y(1); %小于0
+ k, n: |( ~' E* @
y2=y(2); %大于06 V- \9 f8 K: s4 b$ t+ Z
for i=1:n %总迭代次数
& R1 a) Y1 L h3 ^0 a: ~: k
c(i)=(a+b)/2;
# b% D! e1 |. c0 W
f(i)=exp(c(i))+10*(c(i))-2;
\" J* n+ H) G/ z3 b* J
kesai_k(i)=(b-a)/2;
0 e2 q7 s) z3 \$ f
if f(i)>0
& V9 @+ w& u3 n4 P& [; S# F
b=c(i);2 W3 [* s3 h6 O9 F
b1(i)=c(i);8 u- a {$ K( `& M% J0 |$ p6 H7 }
a1(i)=a;$ E& P6 K: s4 @( X3 j
elseif f(i)<01 Y2 v& \3 [/ V, x1 Y2 u% t
a=c(i);; \5 k\" _7 u8 L% Q, Y
a1(i)=c(i);. w8 O. ~' x: D# J: B. e, R\" j
b1(i)=b;
+ `/ A3 M# b4 h; ?1 Y' `
elseif f(i)==0||kesai_k(i)<=wucha
% X# r7 h2 l' X) J/ q( P
disp('精确值解为：');) x# R2 b4 |7 A+ n
disp(c(i));3 G1 U) `5 ^' B3 S
break;$ d: _# Y8 D& }6 ~ M$ S
end; g# x! d5 C5 r! M\" C
end
& ~, K6 {( E9 W! f/ O1 k6 J( [) _; l
disp('迭代次数：');0 `1 |' `) b4 d3 @# t% m8 a
fprintf('%d次\n\n',n);
' B. G! P$ a9 Y; J5 ^( [
fprintf('要求误差%f\n\n',wucha);
' E, f. g; G! e) D/ [, U
disp('输出矩阵为：');
$ R3 s\" a( T+ e4 _( B
A=[a0 a1]';
- m# H2 D3 E+ s1 X* R9 V6 G5 S! z
B=[b0 b1]';- |2 e\" @* I: F8 v
format long. g! ?+ Q% g* k' [
data_out=[A B c' f' kesai_k']1 H$ | X8 @, J6 V
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：: I6 f' Y- s, M! z4 p' X
0.0905
~7 }( j\" X2 T1 R/ r\" }7 [
: s n f; w& c
迭代次数：7 W) h& t, \ p7 @) ]8 C3 {: k
100次. f2 b: m' U- @5 ^* m! ~# o
0 m/ N/ a% _- j3 z- m, E
要求误差0.005000( o9 v5 a4 P, n3 s3 ]% Z
6 H# @9 l- }6 j
输出矩阵为： i' H6 C7 P; u* m4 W6 j! j9 \9 @; a
5 T: O1 R$ q1 ~6 s: C
data_out =
\" o& M* t5 @4 @0 i. e% `8 N; C
7 R. q- P$ }- k2 M7 j E1 g+ N) ]. x
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000% k: }\" \0 I- g, U( h& ]0 {$ [
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000007 s4 x; Y3 j: s2 \2 f4 q
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
, E5 k. _0 Z) |: f7 d# y% b
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
K$ y0 P) l+ ~7 }& c( N
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
; w6 P n7 _5 _% V- Y
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.0156250000000001 h4 O& B1 j1 b3 d/ x- X
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
. S( B L0 N$ ^; V
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000* q* K+ e0 u5 c) E( b! G) h
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000- _ W! q3 `- E- }
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.0009765625000003 v* f* F9 C2 P3 f; w$ R( V
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
! F5 i5 m! G) O8 X r+ k
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
; @4 O3 P/ q# Z/ d/ E% e' ~
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
D# e! s0 B1 |$ L, [
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.0000610351562509 p. E) q+ A Q8 _% c! F
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125# S\" D* O) Q1 s( l% [& l3 \
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063+ ~# z# `' G% | m\" x
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531+ F: j\" J& \; w
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
o6 [+ } t- I( Y0 J8 N0 `
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633& w0 t& a. n: d\" }0 Z% J
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316% W) {; B5 _ q1 R4 {$ Y
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
* G/ W1 J\" A) ^6 L' `+ C
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579& B! |' f! G' V U- B) R
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.0000001192092907 F1 [9 v5 F% n+ b( V5 a8 ^
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645$ |' K( g% `1 U& v+ k2 M! c
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
. x' H6 c' T! T8 I( i
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
( L: ^7 G& v7 _' s. O9 Y
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
5 }; Y& n' C; I$ k5 Y6 ~, X, f
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290\" l/ Z8 ?\" v3 [2 S/ v6 B6 ?
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
- H' ~* X( H7 R H0 X0 Q
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
; K/ b: q, }( S0 b% j! U, C
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661; A s/ ~; R; Y6 Y9 F
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831
2 m4 \* p n) u; t
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
. Q1 j3 }& z5 L2 Q, n' }0 P2 W
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208. D2 K! N1 |/ t/ i) C) q4 A
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104% y( l, X$ E1 X9 B
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
. i5 P4 `+ T7 c8 t4 v
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276- p+ k. i3 ~+ J( F
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036384 K' e/ i: E( k5 i2 P0 e$ f
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819' O- f! c5 j9 d0 [7 {\" Z
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.0000000000009094 ]: U7 I# k3 s
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455; c6 I; ~% C+ }$ i6 C
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227, ]1 S Q3 a/ _9 @. q3 N
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
- e0 z7 ~$ o9 e3 d, r1 k9 ^: I
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
4 K) N7 j k7 p0 m) B! o6 N0 F5 b
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
* k1 V5 p! N8 \- W
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
- u4 d4 w Z. ]
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007( f+ s* F$ T! L8 n( @, D3 {
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
; o1 J5 D4 b8 S5 J, M# S+ i/ t) U# c
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002, l0 t U+ \% A+ ~1 O
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001# U& f\" E, |8 ?8 e0 d/ h
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000