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matlab ÄÚµù Áú¹®ÀÌ¿ä.2

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  • µî·ÏÀÏ 2016-11-02 20:17
  • Á¶È¸¼ö 540
1. ´ÙÀ½ ºñ¼±Çü ¹æÁ¤½ÄÀÇ ±Ù»çÇظ¦ À̺йýÀ» ÀÌ¿ëÇÏ¿© ã¾Æº¸ÀÚ
nf(x)=x^2-4sin(x)
nÃʱâ: a=1, b=3,tol=10^(-5)
nHint:»ç¿ëÀÚ Á¤ÀÇ ÇÔ¼ö¡®f.m¡¯À» Á¤ÀÇÇÏ¿© »ç¿ëÇØ º¸ÀÚ

2.´ÙÀ½ºñ¼±Çü ¹æÁ¤½ÄÀÇ ±Ù»çÇظ¦Newton¹æ¹ýÀ»ÀÌ¿ëÇÏ¿© ã¾Æº¸ÀÚ
nf(x)=x^2-4sin(x)
nÃʱâ:x (±Ù»çÇØ)=3,tol=10^(-5)
nHint1:¾Õ¿¡¼­ »ç¿ëÇß´ø »ç¿ëÀÚÁ¤ÀÇ ÇÔ¼ö¡®f.m¡¯À» »ç¿ëÇÏÀÚ
nHint2: f¡¯(x)=2x-4cos(x)»ç¿ë



3.´ÙÀ½ ºñ¼±Çü ¹æÁ¤½ÄÀDZٻçÇظ¦ÇÒ¼±¹ýÀ»ÀÌ¿ëÇÏ¿© ã¾Æº¸ÀÚ

nf(x)=x^2-4sin(x)
nÃʱâ: x0 (±Ù»çÇØ1)=1, x1 (±Ù»çÇØ2)=3,tol=10^(-5)
n         itermax(ÃÖ´ë ¿¬»ê Ƚ¼ö)=100


nHint:¾Õ¿¡¼­ »ç¿ëÇß´ø »ç¿ëÀÚ Á¤ÀÇ ÇÔ¼ö¡®f.m¡¯À» »ç¿ëÇÏÀÚ


% À̺йý
clear;
clc;
a=1;  % ÃÖÃÊ ±¸°£ ¿ÞÂÊ ³¡
b=3;  % ÃÖÃÊ ±¸°£ ¿À¸¥ÂÊ ³¡
tol=10^(-5); % tolerance
iter=1;
while abs(b-a) > tol
    m=a+(b-a)/2;  % Áß°£ À§Ä¡ ãÀ½
    if  f(a)*f(m) < 0   % ÇØ°¡ ¿ÞÂÊ ¹Ý¿¡ ÀÖÀ½
        b=m;
    else                % ÇØ°¡ ¿À¸¥ÂÊ ¹Ý¿¡ ÀÖÀ½
        a=m;
    end
    x(iter)=m;
    iter=iter+1;
end
iter  % ÃÑ iteration ¼ö
m
f(m)
plot(x, '-ro')
grid on;


% ´ºÅÏ
clear;
clc;
x=3;  % ÃÖÃÊ ±Ù»çÇØ
tol=10^(-5); % tolerance
iter=1;
while abs(f(x)) > tol
    x=x-f(x)/(2*x-4*cos(x));
    xx(iter)=x;
    iter=iter+1;  
end
iter  % ÃÑ iteration ¼ö
x
f(x)
plot(xx, '-ro');
grid on;


% ÇÒ¼±¹ý
clear;
clc;
x0=1; 
x1=3;
tol=10^(-5); % tolerance
itermax=100;
for i=1:itermax
    x2=x1-f(x1)*(x1-x0)/(f(x1)-f(x0));
       if abs(f(x2)) < tol
           break;
       end
    x0=x1;
    x1=x2;
    zz(i)=x2;
end
i  % ÃÑ iteration ¼ö
x2
f(x2)
plot(zz, '-ro');
grid on;


3°¡Áö Áú¹®¿¡¼­ ¹Ø¿¡ »ùÇà Á¦½ÃÇÏ°í ¹®Á¦ Ç®¾î¼­ ÄÚµùÇÏ´Â °Çµ¥ µµ¿ò ÁÖ½Ã¸é °¨»çÇÏ°Ú½À´Ï´Ù.

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