[代码资源] 用对分法解超越方程

[复制链接]

字体大小: 正常放大

seven3069

18 主题	15 听众	945 积分

升级 86.25%

TA的每日心情

	奋斗 2018-11-27 09:23

签到天数: 395 天

[LV.9]以坛为家II

群组: 2016国赛备战群组

电梯直达

1^#

发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

|招呼Ta 关注Ta

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 m) R6 f- w+ |; u
% n=input('请输入迭代次数：');, m8 Z O9 {$ _3 n- i
% qujian=input('请输入初始区间：');3 k. w: f9 E4 i9 w2 j- E& R
n=100;
8 j8 m$ y3 k F8 V& @, G) w
wucha=0.005;
7 Y' \4 F' H) I$ p3 h9 u- P& ?
qujian=[0 1];
- r2 W: g\" `/ Q; y4 o5 R) k7 Q
a(1)=qujian(1);
) B; m: g) S: b4 B9 W5 M+ e
b(1)=qujian(2);
' {) X, q- X\" @& }0 {
a0=a(1);
5 C7 H9 h5 m) s\" T- l
b0=b(1); T& Q$ _1 l: Q- D: x! ?
x=qujian;
) B3 P2 C: X\" `5 M
y=exp(x)+10*x-2;\" u& o7 K6 a; [2 E
y1=y(1); %小于0
# a% S/ h! N5 V
y2=y(2); %大于0
: x, H- ]0 ]7 B+ V3 m2 j5 \; k
for i=1:n %总迭代次数8 b+ q9 k# n( k: _- S; s* v
c(i)=(a+b)/2;
6 U8 o; {# U- ?( A, q$ j
f(i)=exp(c(i))+10*(c(i))-2;5 X2 h/ A& t0 F5 @5 Y2 ~
kesai_k(i)=(b-a)/2;
) i0 o5 O\" q. y\" G\" a- D/ `
if f(i)>0
3 S, `5 }- a\" d3 k
b=c(i); h. ^. ^, q; V# X+ S- m# Z
b1(i)=c(i);
6 `$ E' C, t+ g C& W
a1(i)=a;
\" n. d' n+ j\" M G: Q6 L: _7 \
elseif f(i)<0
# \) Y. l! P6 w5 ~/ o% |
a=c(i);# `6 I/ I% w# B) R- R1 x4 ]
a1(i)=c(i);
; b+ U1 A' D1 y# U- V
b1(i)=b;/ D\" W6 `8 }\" W' T+ |- B* ]* \
elseif f(i)==0||kesai_k(i)<=wucha
, T' p2 z w& D( T9 P$ E( K
disp('精确值解为：');
, M- s. h8 j0 e4 g( c P( v
disp(c(i));
break;
$ ?$ }1 g1 k5 z\" a: H, g
end
6 r/ R$ R! k6 l, K( ]
end
0 T! M! e/ o; u
disp('迭代次数：');0 j+ }# b) k c \& \3 Y1 i0 X
fprintf('%d次\n\n',n);, D& }% s5 \) r7 b9 r1 ~9 \
fprintf('要求误差%f\n\n',wucha);! g+ [0 p6 i5 V/ _' x& [
disp('输出矩阵为：');5 @9 G% {! o c
A=[a0 a1]';5 N I) ?' ?; @- b0 C6 S0 i# q
B=[b0 b1]';
7 ^, M$ Q: h* Y* ]- w) |
format long& |. ^/ Y p2 O* W, M% v% S
data_out=[A B c' f' kesai_k']
& d5 l4 x6 A- }/ W
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：
\" q7 a Q* n$ }0 C$ r' Y
0.0905. R$ N+ V7 p2 R( h
0 z. O4 g$ |# ~
迭代次数：
9 r# P& A' ?1 E) ?0 H
100次
8 z: c% V/ _6 b7 a( L, W
1 j# @0 S M/ U# E
要求误差0.005000
8 v1 j. }5 u% t d$ Z6 f' e
/ O& S* s( `3 U2 X5 c/ B2 C
输出矩阵为：4 C0 C' B2 t0 y: ]/ f+ e
7 d. M, {& I) z3 t
data_out =
' p* i8 x$ ~6 N% T( y
5 t! A) Y$ q K2 N- m& R
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000
% B' B' ]3 f: M9 l% ], Z8 s
0 0.500000000000000 0.250000000000000 1.784025416687741 0.2500000000000009 f# b, }1 U- ~4 I7 i
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
$ b, k( K2 p2 U+ H
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000: d\" ~9 n: {( e. y2 ]% P
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000\" {8 d( H. k1 x: v* x
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
+ D# M$ t# a- D( [ \' P
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.0078125000000002 ~8 [# a6 F\" T# b. B\" ]. J% t- q
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
/ M0 S: C2 B1 f& X! u ]* U\" z
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
2 @2 h7 S\" [4 \- s1 s# Q; o
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000. v- j* H- _ ?\" v$ i
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.000488281250000
. ?8 c) i- \3 \9 y
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
0 l2 p' I% U5 v& w) x, T
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.000122070312500
% _. N4 ?/ R9 a- g% Z
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250
' n3 D7 I1 [) x
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.0000305175781257 \6 k% q7 Z4 M\" |5 n& b3 h
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
7 T, o% P0 _2 l, c
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531
# g) U8 y2 G8 a; n+ `9 _( |5 H0 U: v' L
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.0000038146972660 o: c- A5 @7 v' S3 {, [( Q/ o' y
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633; `$ H9 y6 o3 @. _
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
\" ^) w; G( G- C3 u ]5 q
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
, J$ i/ I8 W$ U9 S: ?, B
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579, _5 A, y; e8 a8 Z3 O5 k
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290\" m* w& Y7 ` O) k6 v/ R: e
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645& H1 Y: z8 N2 X+ o+ U0 N2 J
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
% j, i6 w9 h# C9 r1 k$ h* q
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.000000014901161
7 O\" \2 r# r8 v: X0 a5 K
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581
& p, m( \ V8 M. D
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.000000003725290
/ t- |& f6 S5 k\" ~6 M; u7 ?+ m: E
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.000000001862645# P3 v! w! d8 H$ H
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.0000000009313235 e8 c, \& ~+ h9 w0 O6 ?9 Z
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661
2 {+ U# {! `+ q8 G) @7 }3 ?! ~
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.000000000232831\" k$ d4 r1 o0 \( \& C
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.0000000001164155 g+ }8 J9 e) `( }8 u1 X& P) i
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.000000000058208
; ^' E ?6 ^' I9 k
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104* Y5 h& ^7 I1 I: ]! a8 Y
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.0000000000145521 J% p8 E# F\" j- n9 e' N3 v% ], |
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.000000000007276
+ S) A2 b3 y0 o3 B# ]+ q, p
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638, Y+ U) {6 Q8 t\" w& w\" f' I
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
' D( B. @; X& S5 A& e3 |4 e* Z0 [
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909+ X( f4 B5 s$ ]# `% D
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455) F; ]# q& k( i& B. p3 b, i4 T
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
# Z' F5 y7 |# ^* a* ?2 o
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
) T7 f. h: v4 l
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
$ }; M4 E/ h- b, @0 s) W
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.0000000000000285 s& P8 G) r6 |: ?9 }1 _: Z: u6 y
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014
2 Z2 I\" M# G, \ ], L1 g p
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.000000000000007
2 l z, w' E' c4 g$ N
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004
0 F4 I, b. b0 ?4 b0 e5 R' o
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002
5 |/ S+ m7 `, {& t, X- l\" z& C7 W
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.000000000000001
0 M& G8 E\" d% C# P; B$ h6 o
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000