nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

C.2 Code for the Newton-Raphson Method 167
real(V_14),imag(V_14),’*b’,real(V_15),imag(V_15),’*b’,
real(V_19),imag(V_19),’*b’,real(V_20),imag(V_20),’*b’,
real(V_39),imag(V_39),’*b’,
real(V_40),imag(V_40),’*b’)%k,0,’b’...
axis([-1 1 -0.5 0.5 ])
Title(’Plot of eigenvalues for the Jacobian evaluated in
the upper inflamed region’)
xlabel(’real(eig)’)
ylabel(’img(eig)’)
%--------------------------------------
C.2 Code for the Newton-Raphson Method
The code for the Newton-Raphson method. This is adapted from Shampine et al.
(2003).
function root = newtonRaphson2(func,M,tol)
% Newton-Raphson method of finding a root of simultaneous
% equations fi(x1,x2,...,xn) = 0, i = 1,2,...,n.
% USAGE: root = newtonRaphson2(func,x,tol)
% INPUT:
% func = handle of function that returns[f1,f2,...,fn].
% x = starting solution vector [x1,x2,...,xn].
% tol = error tolerance (default is 1.0e4*eps).
% OUTPUT:
% root = solution vector.
%define global
%global g;
Q=M;
if nargin == 2; tol = 1.0e7*eps; end %NARGIN defines the
number of input arguments that were used to call the function
(M,tol). %Tol is the error tolerance for the computation
here set to 1.0e4*eps = 2.2204e-012
%if size(M,1) == 1; M = M’; end % M must be column vector
(ctranspose - Complex conjugate transpose [’] ). if 3==1??
%for i = 1:50