[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 |正序浏览

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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) E% R# {\" S$ {% T! @$ v
% n=input('请输入迭代次数：');
\" t( J4 f7 D& }6 ?/ p) g
% qujian=input('请输入初始区间：');, J% A7 u8 e5 S+ X7 p
n=100;
. o4 p: e\" A. Q& k
wucha=0.005;
# O, c, q5 w* i0 V
qujian=[0 1];2 G- J G0 j/ p1 a( s* _6 T+ }
a(1)=qujian(1);
# n8 J. i- @- F$ U
b(1)=qujian(2); 2 X\" H( l8 y6 `' H$ P0 K+ q# M
a0=a(1);7 p4 N, e; f5 O
b0=b(1);
7 f' I X% s, c3 r0 f7 f\" X: w
x=qujian; w; ~7 |) ^4 f* M; R! m) z8 k\" c
y=exp(x)+10*x-2;7 R8 ?) u; x\" Y6 x0 A9 [2 P
y1=y(1); %小于0
7 w7 s+ M! I3 J4 b S' e0 F6 \\" Z
y2=y(2); %大于00 i* [) B1 B9 o2 d
for i=1:n %总迭代次数+ W. ^2 u- n& @5 {) i
c(i)=(a+b)/2;8 ]3 [' {; V T, J
f(i)=exp(c(i))+10*(c(i))-2;
8 p! k* x5 B- d
kesai_k(i)=(b-a)/2;; g$ f, L+ S5 w7 |. Q9 j$ i* `* q
if f(i)>0
\" R\" Z& |# f\" W+ u
b=c(i);
8 W7 Q% n\" p; g4 j* i, }\" a
b1(i)=c(i);
* ~* _% q7 [0 Z3 P% k# }# }% v
a1(i)=a;
% B1 A n+ Z5 Q8 ^
elseif f(i)<0- S- A+ ?' f% N& v. t/ `: I
a=c(i);
7 V\" G* H$ i3 e. @9 |
a1(i)=c(i);' f& B$ K' e6 J& Y
b1(i)=b;6 n$ D7 ~; v+ I, a3 z) z
elseif f(i)==0||kesai_k(i)<=wucha& |0 d\" l E; R# w* r
disp('精确值解为：');( S+ O# k! h2 h$ V, G# f0 g8 }\" w. E
disp(c(i));1 n/ N* e\" b) z% l0 @
break;
0 W6 I f. g q; z- I+ N. e# U# u
end8 w: X/ ?1 a3 j% b
end8 N/ Y& d0 h, x& p\" K\" A
disp('迭代次数：');: V F- N7 I& J$ l T [$ l- k# n
fprintf('%d次\n\n',n);
) S/ b, n) O/ R\" ~
fprintf('要求误差%f\n\n',wucha);/ m* r1 v5 e7 p! Y8 Z* A
disp('输出矩阵为：');
\" u$ G7 v: ^) a# M0 E2 {
A=[a0 a1]';! X2 z- ^) W( {
B=[b0 b1]';
' n- w$ {7 w# X9 [/ b
format long
data_out=[A B c' f' kesai_k']
! M8 t% [, Z, w. z& ?) m6 g
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：
6 E; K6 R4 r' n1 ? z& M
0.09057 P# [) M& l. e2 J/ q6 H
0 r& X) Y5 ~. n- e* f, c
迭代次数：
: E% b* B0 ^! G: A1 b- t; m$ S/ d+ F
100次
|4 a# P/ }% J; P7 z
. _) l6 W, K0 [, ^$ }% C
要求误差0.005000\" w/ k1 o7 h\" `; ~3 T3 g
& _: |) E/ H8 \% U
输出矩阵为：
' S% l- l6 `/ s$ D8 V0 g
) g+ m9 V! n, h/ J\" d
data_out =. k1 l3 |+ c: r, s
5 k' [) G) ]9 n6 f7 r7 f
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
$ v3 a! E; A* K) E1 D; F
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000( ?8 m3 ^\" w0 t
0 0.250000000000000 0.125000000000000 0.383148453066826 0.1250000000000005 x! h0 ?6 K1 x2 A
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
; V\" L/ }. v) h\" k$ n- F
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.0312500000000002 I# D5 J' l3 Y1 ^$ |% k U
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
* @1 }; Y. h( R5 ]5 w9 n
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000
. z\" @# W- J8 q% U. \, k
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
, U\" ]* m- g/ z( v8 {2 `1 R1 M6 p0 a
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000/ K8 K; h5 D; r* I& Y2 d2 e
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000
+ Z5 j- b9 ^+ R6 W
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
* g) D9 G* Y: F& P\" Q
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
' ]; U- k$ n6 }& c# w9 g
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
+ e4 F/ x& r+ M; [ p/ l( R8 _2 J
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250, `' p; Z4 |7 m8 Z
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125- F9 a7 ^9 @\" C
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
, q( Q; m! N$ X8 w, v' n& V% _4 `: r
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
9 p: E$ Z6 D* E. G! Y8 e
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266+ m X p4 \( t0 v# Q4 X/ Y' N) ~
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
) d; W: l. X% B0 M3 y3 x
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158 H# k Q0 \& \
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579- r8 z7 i' j7 a
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290' Z# p( h$ r- E: Z0 v' Q; {
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.0000000596046454 e' d) {0 C2 f- q
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322, E: z\" \2 G1 @: t, k! @) J
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161. c% s6 {8 h1 [) r, u; R( |3 W; D
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
, A% y! B# s2 ~: f V7 ^
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
0 e( j4 x q4 d& k @* |
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645
1 o, S0 x1 r/ y* S7 `& ~
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
. J1 e5 |+ R) w5 t8 t
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
$ H1 w, S0 s+ u; [3 |& v8 s
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831; {- q& K5 `% G
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415# _' N% H6 T: X% v0 G' N3 J3 E. W
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582088 \2 d+ g9 A/ k |: r, F( P
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.0000000000291040 }3 w% X X/ y
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145525 U\" K# b0 p/ U/ o/ g
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
% D4 V. |# }+ b2 P7 G/ Q, v# B9 G
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638
- M6 |* B3 x6 S* A
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.0000000000018198 M8 _& v' S) ^. n% O; h) f
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909# K/ H0 C6 V+ V0 I6 J
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
# x. P$ i7 V4 ^+ O
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.0000000000002275 X2 q8 l& p1 U/ _7 g6 [3 L* t) W
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114% o% C9 L- I6 M8 ]/ \: |5 ~
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
/ r. d v2 f w) w. x1 f1 \
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028- B) C1 m, i0 j0 y( ?\" x
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.0000000000000146 a! u& E6 J L1 g: x; @
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
# }' A: S9 N- M\" j\" N& _8 T8 ?
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
. C n. |% Z2 k. z# B% v
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
$ ]& l- _! n! ]
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000011 ^1 k+ n# S( W w* N
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000