Matlab实现数值分析中的算法以及相应的实验报告

%A=input("输入系数矩阵："); %d=input("输入常数向量"); % option=input("顺序高斯LU分解选1，列主元LU分解选2: "); % A= [0.3e-15,59.14,3,1,59.17; % 5.291,- 6.13,- 1,2,46.78; % 11.2,9,5,2,1; % 1,2,1,1,2 ]; % A=[1,2,2;4,4,2;4,6,4]; function[L,U,x]=LU_GaoSi(A,b) option=input("顺序高斯LU分解选1，列主元LU分解选2: "); [n,m]=size(A); if m~=n error('error'); end for k=1:n if option==2 s=k; for i=k+1:n if abs(A(i,k))>abs(A(s,k)) s=i; end end if s~=k for j=1:n m=A(k,j); A(k,j)=A(s,j); A(s,j)=m; end t=b(s); b(s)=b(k); b(k)=t; end end if A(k,k)==0 disp('error'); continue; end for i=k+1:n A(i,k)=A(i,k)/A(k,k); for j=k+1:n A(i,j)=A(i,j)-A(i,k)*A(k,j); end end end L=zeros(n,n); for i=1:n L(i,i)=1; end for i=2:n for j=1:i-1 L(i,j)=A(i,j); end end U=zeros(n,n); for i=1:n for j=i:n U(i,j)=A(i,j); end end %Ly=d y=zeros(n,1); y(1)=b(1); for k=2:n y(k)=b(k)-L(k,1:k-1)*y(1:k-1,1); end %Ux=y x=zeros(n,1); x(n)=y(n)/U(n,n); for k=n-1:-1:1 x(k)=(y(k)-U(k,k+1:n)*x(k+1:n,1))/U(k,k); end end