线性方程组matlab程序.doc

程序3-1 function[x,index]=Gauss(A,b) [m,n]=size(A); if m~=n disp(Argument matrix A must be square!); index=0; return; else if m~=length(b) disp(The dimentions of Aand b do notagree!); index=0; return; end; Ab=[A b]; index=1; for k=1:n-1 if Ab(k,k)==0 disp(index=0) index=0; return end; Ab(k,:)=1/Ab(k,k)*Ab(k,:); for i=k+1:n Ab(i,:)= Ab(i,:)-Ab(i,k)*Ab(k,:); end end if Ab(n,n)==0 disp(index=0) index=0; return end Ab(n,:)=1/Ab(n,n)*Ab(n,:); x(n)=Ab(n,n+1)/Ab(n,n); for j=n-1:-1:1 x(j)=(Ab(j,n+1)-Ab(j,j+1:n)*x(j+1:n))/Ab(j,j); end end return 运行与结果： A=[1 2 3;4 5 6;7 8 0]; b=[1 1 1]; [x,index]=Gauss(A,b) x = -1 1 0 index = 1 程序3-2 function[x,det,index]=GaussSys(A,b) [m,n]=size(A); if m~=n disp(Argument matrix A must be square!); index=0; return; elseif m~=length(b) disp(The dimentions of A and b do not agree!); index=0; return; end Ab=[A b];det=1;index=1;x=zeros(n,1); for k=1:n-1 [amax,imax]=max(abs(Ab(k:n,k))); if amax==0 disp(The Linear System is singular!); index=0; det=0; return; elseif k~=imax+k-1 Ab([k imax+k-1],:)=Ab([imax+k-1 k],:); end for i=k+1:n Ab(i,:)=Ab(i,:)-Ab(i,k)*Ab(k,:)/Ab(k,k); end det=Ab(k,k)*det; end if Ab(n,n)==0 disp(The Linear System is singular!); index=0; det=0; return; end det=Ab(n,n)*det; x(n)=Ab(n,n+1)/Ab(n,n); for k=n-1:-1:1 x(k)=(Ab(k,n+1)-Ab(k,k+1:n)*x(k+1:n))/Ab(k,k); end 运行与结果： A=[1 2 3; 4 5 6;7 8 0]; b=[1 1 1]; [x,det,index]=GaussSys(A,b) x = -1.0000 1.0000 -0.0000 det = 27.0000 index = 1 程序3-3 function[x,index]=GaussJor(A,b) Ab=[A b]; [m,n]=size(A); if m~=n disp(Argument matrix A must be square!); index=0; return; elseif m~=length(b) disp(The dimentions of A and b do not agree!); index=0; return; end index=1; x=zeros(n,1); det=