用最速下降法数值求解线性方程组

%Fastest descent method is realized by this function below function y=FDM(A,b) [row_num,column_num]=size(A); length_b=length(b); if row_num ~= column_num disp('The number of rows of the coefficient matrix is not equal to its number of columns') return elseif row_num ~= length_b disp('Please ensure the dimensions of the coefficient matrix is equal to the dimensions of inhomogeneous terms') return end if row_num>2 for i=1:row_num-1 for j=i+1:num if A(i,j)~=A(j,i) disp('The coefficient matrix is not a symmetric matrix') return end end end end for i=1:length_b Sequential_master=zeros(i); for j=1:i for k=1:i Sequential_master(j,k)=A(j,k); end end if abs(det(Sequential_master))<10^(-9) disp('The coefficient matrix is not a positive-definite matrix') return else continue end end [r_b,c_b]=size(b); if c_b>1 b=b'; end x=zeros(row_num,1); iterations=0; while (A*x-b)'*(A*x-b)>10^(-9) || iterations>10^6 r=b-A*x; alfa=(r'*r)/(r'*A*r); x=x+alfa*r; iterations=iterations+1; end txt=['Iterating ',num2str(iterations),' times']; disp(txt) y=x;