Analysis by SBC

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이창대

Subject

연습 1-13 입니다

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사진3.jpg (31 KB) - Download : 107

% hwk1_1e.m
% Find all roots of f(x) = exp(x)-x-2
%   using Bisection, Newton and Secant methods
%
function hwk1_1e
tol=10^(-8);
% Plot
ezplot(@f,[-2,2]); grid
return
% Guess intervals for roots
% [1.0,1.5], [-2.5,-1.5]
% Call Bisection method
x = [];
x = [x, bisect(1.0,1.5,tol)];
x = [x, bisect(-2.5,-1.5,tol)];
xb=x;

% Call Newton method
x = [];
x = [x, newton(1.25,tol)];
x = [x, newton(-2,tol)];
xn=x;

%Call Secant method
x = [];
x = [x, secant(1.0,1.5,tol)];
x = [x, secant(-2.5,-1.5,tol)];
xs=x;
disp('')
disp('')
disp('The roots by Bisection, Newton and Secant methods')
[xb; xn; xs]'

%%%%%% Define functions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function y = f(x)
    y = exp(x)-x-2;
function y = fp(x)
    y = exp(x)-1;
%%%%%% bisect Methods %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function c=bisect(a,b,tol)
  fprintf('------------------------------------ \n')
  fprintf(' n     a     b    c    f(c) \n')
  fprintf('------------------------------------ \n')
  n = 1; c = (a+b)/2;
  fprintf('%3.0f %12.8f %12.8f %12.8f %12.4e \n',n,a,b,c,f(c))

  while( abs(f(c))> tol )
      if f(b)*f(c)>=0, b=c; else, a=c; end
      n=n+1; c = (a+b)/2;
  end
  fprintf('%3.0f %12.8f %12.8f %12.8f %12.4e \n',n,a,b,c,f(c))
%%%%%%%%%% Newton method%%%%%%%%%%%%%%
  function x=newton(x,tol)
  fprintf('------------------------------------ \n')
  fprintf(' n     x     f(x) \n')
  fprintf('------------------------------------ \n')
  n = 1; x= x - f(x)/fp(x);
  fprintf('%3.0f %12.8f %12.4e \n',n,x,f(x))
  while ( abs(f(x))>tol )
      n=n+1; x= x - f(x)/fp(x);
  end
fprintf('%3.0f %12.8f %12.4e \n',n,x,f(x))
%%%%%%%%% Secant method%%%%%%%%%%%%%%%%
  function x2=secant(x0,x1,tol)
  fprintf('------------------------------------- \n')
  fprintf(' n     x     f(x) \n')
  fprintf('------------------------------------- \n')
  n = 1; x2= x1 - f(x1)*(x1-x0)/(f(x1)-f(x0));
  fprintf('%3.0f %12.8f %12.4e \n',n,x2,f(x2))
  while ( abs(f(x2))>tol )
      x0=x1; x1=x2;
      n=n+1; x2= x1 - f(x1)*(x1-x0)/(f(x1)-f(x0));
  end
fprintf('%3.0f %12.8f %12.4e \n',n,x2,f(x2))

실행결과
------------------------------------
n     a     b    c    f(c)
------------------------------------
  1   1.00000000   1.50000000   1.25000000  2.4034e-001
25   1.14619321   1.14619324   1.14619322  1.2681e-009
------------------------------------
n     a     b    c    f(c)
------------------------------------
  1  -2.50000000  -1.50000000  -2.00000000  1.3534e-001
25  -1.84140569  -1.84140563  -1.84140566 -4.4001e-010
------------------------------------
n     x     f(x)
------------------------------------
  1   1.15349002  1.5744e-002
  3   1.14619322  2.3681e-009
------------------------------------
n     x     f(x)
------------------------------------
  1  -1.84348236  1.7477e-003
  3  -1.84140566  1.2879e-014
-------------------------------------
n     x     f(x)
-------------------------------------
  1   1.11149143 -7.2604e-002
  5   1.14619322 -3.8866e-010
-------------------------------------
n     x     f(x)
-------------------------------------
  1  -1.82233341 -1.6018e-002
  4  -1.84140566 -7.4809e-011
The roots by Bisection, Newton and Secant methods

ans =

   1.14619322121143   1.14619322172397   1.14619322043949
  -1.84140565991402  -1.84140566043698  -1.84140566034805

DATE: 2013.04.15 - 15:37

LAST UPDATE: 2013.04.15 - 15:39

4.11

1장1(e)번 입니다.