编写一个一般均衡函数系统

Question

我正在尝试创建一个方程组，它在理论上代表下面看到的函数（我们知道 Kt、alpha 和 beta，但不知道 Kt+q） - 非常感谢任何帮助：

我应该如何表示并将其传递到我的 newton raphson 代码中（这里的任何输入也值得赞赏）：

% 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

Answer 1

我认为您需要执行以下步骤：

1. 将每个函数表示为 f(k) = 0：从每个方程的两边减去 RHS。
2. 计算线性增量的雅可比：J*dk = f
3. 对未知的 k 向量进行初步猜测
4. 求解未知增量向量 dk
5. 更新向量 k：k(new) = k(old) + dk
6. 迭代收敛