Matlab 编写一般均衡函数系统

Matlab 编写一般均衡函数系统,matlab,math,newtons-method,Matlab,Math,Newtons Method,我试图创建一个方程系统,理论上表示以下函数(我们知道Kt、alpha和beta,但不知道Kt+q)-非常感谢您的帮助: % newton raphson function I = NR(f,x0) x=x0; %starting point fx=f(x); J = CDJac(f,x); I = x - fx/J; end % the jacobian below is validated; function [DCD] = CDJa

我试图创建一个方程系统,理论上表示以下函数(我们知道Kt、alpha和beta,但不知道Kt+q)-非常感谢您的帮助:

% newton raphson 
function I = NR(f,x0) 
    x=x0; %starting point 
    fx=f(x);  
    J = CDJac(f,x); 
    I = x - fx/J;     
end 

% the jacobian below is validated;

function [DCD] = CDJac(f,xbar)%the jacobian 
    jk=length(xbar); %find the dimension of x
    hstar=eps^(1/3); %choose value of h based upon Heer and Maussner machine eps
    e=zeros(1,jk); %1 x j vector of zeros; j coresspond to the derivative 
    %with respect to the jth varibale. If j=1, I am taking the derivative of
    %this multivraite function with respect to x1. Creates a bunch of zeros. AS
    %we go through and evlaute everything. We replace that zeros with a one. 
    for j=1:length(xbar) %if j is 1:10. xbar is the vector of 
        %10 different points. you have 10 differetn x s. 
        e(j)=1; %replace the jth entry to 1 in the zero vector. (1,0). In a 
        %of loop, j become 2 after it is done with 1. We then take the second
        %element of it and change it to a 1- (0,1). 
        fxbarph=f([xbar+e.*hstar]); %function evaluated at point xbar plus h
        fxbarmh=f([xbar-e.*hstar]); %function evaluated at point xbar minus h
        DCD(:,j)=(fxbarph-fxbarmh)./(2*hstar);
        e=zeros(1,jk); %create the ej row vector of zeros. For instance, when j
        %goes to 2, you need to have 0s everywhere except the second column. 
    end
end

我应该如何表示这一点并将其传递到我的newton raphson代码中(这里的任何输入也非常感谢):


我认为您需要执行以下步骤:

  • 将每个函数表示为f(k)=0:从每个方程的两侧减去RHS
  • 计算线性增量的雅可比数:J*dk=f
  • 对未知的k向量进行初始猜测
  • 未知增量向量dk的求解
  • 更新向量k:k(新)=k(旧)+dk
  • 迭代收敛