[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 |! q# b3 U( z0 L/ F9 t4 V
% n=input('请输入迭代次数：');# ]- Z/ r: X7 o D0 T! c* A
% qujian=input('请输入初始区间：');1 ~! n\" _\" E\" u% u' H4 Z
n=100;. ^2 ^4 T6 |) n0 h, w& p
wucha=0.005;6 x9 J: Z/ X$ e* s4 r1 s
qujian=[0 1];* A4 _' r7 g5 M/ Y
a(1)=qujian(1);$ {* k3 [- s* w' N
b(1)=qujian(2);
. l7 T$ @# ^. G3 W
a0=a(1);
# t: N: H9 ]3 {8 c& \9 }
b0=b(1);
: W' p1 `1 ? z* d. @
x=qujian;9 [5 j) K4 a% B
y=exp(x)+10*x-2;* }* l5 S0 P8 v; w( i& b
y1=y(1); %小于0
7 o+ X. k1 O* }5 n\" X- s
y2=y(2); %大于0
3 d3 {* Z8 t! q/ {; z
for i=1:n %总迭代次数+ U5 ]% m6 L$ T, j
c(i)=(a+b)/2;& d; S: p\" _- v
f(i)=exp(c(i))+10*(c(i))-2;
: K1 ^) \/ j3 c4 L
kesai_k(i)=(b-a)/2;7 Z. o- j& Z( [* z: _- ?\" h$ i
if f(i)>0
' I& N: q0 v; a$ P
b=c(i);8 ^% A6 u2 m$ } Q+ w& q1 Q
b1(i)=c(i);8 F\" M0 c; u6 I5 L; O4 p, x
a1(i)=a;7 h2 ]$ ? ^' N0 r% T
elseif f(i)<0
/ a) W& [0 d2 [, X
a=c(i);
9 O, B1 P! P3 [) i
a1(i)=c(i);
0 ^; S% h; I0 B2 K: x4 s
b1(i)=b;
1 h7 T, ^. [$ S3 x) @8 G
elseif f(i)==0||kesai_k(i)<=wucha5 N! `& l( s6 I! D
disp('精确值解为：');2 Y5 d: x, v1 E( e H2 C# G
disp(c(i));
* K4 l& C. o, r% @) W4 n% G' \* U, ~
break;
! u* c1 w/ N5 }! B. ^
end4 a- b! G7 m1 s
end
R) ]: I7 e$ u U+ v5 G# P8 n9 E
disp('迭代次数：');# r v' r: ^ Y& \5 J\" Q8 S
fprintf('%d次\n\n',n);
+ _8 l& {1 \1 g- _
fprintf('要求误差%f\n\n',wucha);2 x% @, g1 ], Y1 J
disp('输出矩阵为：');9 [; Q* z- n8 n0 N. A2 e
A=[a0 a1]';
0 ?$ K/ X2 l2 R\" s\" S2 s0 ]. ]) @/ D
B=[b0 b1]';5 f: }7 c% I# ^9 N# x4 Q
format long
, n' j8 z% B5 d) S) x
data_out=[A B c' f' kesai_k']
$ n/ U- m* d\" B- Z! e
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：+ F- }. }+ T: T) L4 B
0.0905
( F& g0 B5 F9 q h! K
) o1 ]1 S* A# v ]) N, C0 w D
迭代次数：8 z* e0 E# E0 ]. \# _
100次
M0 u$ N- Y7 p
8 `- `( y! b6 _: I
要求误差0.005000, k- m$ l% g3 v3 |1 u; D. Z
5 |) ]! ~1 c: O {! }6 S1 B+ Z
输出矩阵为：- }. R5 |* t e) t
/ ?- g\" Y& u1 Z! G, x1 P
data_out =3 U6 i0 o/ k- U: X- b% H
7 U7 t- o% N1 k9 h5 u$ G
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000+ |; u0 D4 h# ]2 k! Q. {
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000
$ c; b: _. P3 v+ a2 `\" O8 q
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000$ l4 ?& C% y6 B$ Z$ f3 s
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000% a/ ^9 o4 ^3 S% u
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000
1 ^9 @5 e b; M& ?) B- z) g
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
# [6 @5 d1 A2 z; i! U' |
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000002 l1 H* Y7 g1 U# A; Y
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
: d; c( D$ b% H7 w
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
2 f2 n/ K8 h# s\" ^# w& e+ R1 F
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000, n0 O$ W6 w* @8 _5 j0 \
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000) n( y% s& y: n( e9 n
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
1 z! Z! W/ p. u$ y+ p
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
, \; H7 w1 m. S/ a( `
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250& s6 L- l C* A+ v\" i
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
D/ L* K& O K/ j( \3 `
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063. Y) z; F! k$ ?* E3 H9 w
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.0000076293945313 F3 ?! Z- S( o
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266
9 k% z- s7 U, |# O4 b/ x' k
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.0000019073486330 y7 ]6 [, ]' S% W; U$ {
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
5 `8 c4 U* V) _4 E
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158 P3 D6 Z4 f/ \/ Z' G0 n+ q1 c
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579! T1 B. \ D& u; I7 i1 l
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
; I, a' Q\" V* s2 P0 T5 z& p
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
* f( v1 k5 |3 q
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322! Q/ O& Q- K# F( l$ I
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.0000000149011617 ?2 Y9 c! x5 L, v Y4 X
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
+ G* G5 ~7 [& f7 I
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
( w\" R6 L x\" H J$ c% H7 O
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
4 j. s/ f$ f1 H1 [ [, I. K, o
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323' V/ A4 K; r7 |8 x
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661+ w\" V& r2 s8 [: E( ]5 {. G7 l$ Z
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328318 s' G( g; e5 V8 H
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415\" y\" A D: F8 A2 B- D% z2 t8 _
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
5 d) u, l% u% z; K' X
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
\" r- p3 m. J {0 k9 E) n, l7 }
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552 _* f0 @! l3 \; @
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276: R/ e, V7 K& [6 c6 P0 Y
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.0000000000036385 A2 t- J3 I/ ~9 E+ \
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
5 I) u7 X( \6 ]/ M L( l; |
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
/ S x! M5 `3 I
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455( C* H9 Y8 f+ D4 C
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
& C3 k$ [/ J; \1 R- l; u3 h
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
2 N) Z7 m5 p' V
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
9 q4 |, ~3 S% X1 o
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
8 Q, z6 \- v\" J3 F6 p7 N
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
/ ^ w Q6 d7 }! O3 G1 @- g
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.0000000000000041 d+ c& X5 q: _) ]7 z
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002; S1 Z5 Z7 t6 X# Q5 G% ~6 @' R
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
' \* Z4 Y$ _' ^( |# V& F
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000