列主元高斯消去法、LU三角分解法、龙贝格(Romberg)算法、最小二乘法的Matlab程序及运行结果

1、1 列主元高斯消去法M文件functionx=gauss(a,b) n=length(a); x=zeros(n,1); a=a b; for k=1:n-1 max=k; for i=k+1:n if a(i,k)>a(max,k) max=i; end end temp=a(k,k:n+1); a(k,k:n+1)=a(max,k:n+1); a(max,k:n+1)=temp; for i=k+1:n a(i,k)=-a(i,k)/a(k,k); a(i,k+1:n+1)=a(i,k+1:n+1)+a(i,k)*a(k,k+1:n+1); end end x(n,1)=a(n,n+

2、1)/a(n,n); for i=n-1:-1:1 sum=0; for j=i+1:n sum=sum+x(j,1)*a(i,j); end x(i,1)=(a(i,n+1)-sum)/a(i,i); endMatlab运行结果2LU三角分解法M文件function y=LU(A,B); n=length(A); A=A B; for k=1:n-1; for i=k:n; if(abs(A(i,k)=max(abs(A(k:n,k) P(k)=i; temp=A(k,:); A(k,:)=A(i,:); A(i,:)=temp; end end for j=k+1:n; A(j,k)=A(

3、j,k)/A(k,k); A(j,k+1:n+1)=A(j,k+1:n+1)-A(j,k)*A(k,k+1:n+1); endendP(n)=n; L(1,1)=1; L(2:n,1)=A(2:n,1);L(1,2:n)=0;U(1,1)=A(1,1); U(2:n,1)=0;U(1,2:n)=A(1,2:n); for i=2:n; L(i,1:i-1)=A(i,1:i-1); L(i,i)=1; L(i,i+1:n)=0; U(i,1:i-1)=0; U(i,i:n)=A(i,i:n);end x(n) = A(n,n+1)/U(n,n); for k = n-1:-1:1 x(k)=A(

4、k,n+1);for p=n:-1:k+1;x(k) = x(k)-U(k,p)*x(p); end x(k)=x(k)/U(k,k); endxLUPEndMatlab运行结果3龙贝格(Romberg)算法M文件functiont=romberg(f,a,b,e) t=zeros(15,4); t(1,1)=(b-a)/2*(f(a)+f(b); for k=2:4 sum=0; for i=1:2(k-2) sum=sum+f(a+(2*i-1)*(b-a)/2(k-1); end t(k,1)=0.5*t(k-1,1)+(b-a)/2(k-1)*sum; for i=2:k t(k,i)

5、=(4(i-1)*t(k,i-1)-t(k-1,i-1)/(4(i-1)-1); end end for k=5:15 sum=0; for i=1:2(k-2) sum=sum+f(a+(2*i-1)*(b-a)/2(k-1); end t(k,1)=0.5*t(k-1,1)+(b-a)/2(k-1)*sum; for i=2:4 t(k,i)=(4(i-1)*t(k,i-1)-t(k-1,i-1)/(4(i-1)-1); end if k>6 if abs(t(k,4)-t(k-1,4)<e disp('答案 ',num2str(t(k,4); break; end end end if k>=15 disp('溢出'); end Matlab运行结果4最小二乘法M文件functiona,max,det=zuixiaoerchengfa(x,y,r) n=length(x); c=ones(n,r+1); for i=2:r+1 for j=1:n c(j,i)=x(j)(i-1); end end A=c'*c; b=c'*y' a=inv(A)*b; det=0; max=0; for i=1:n sum=a(1); for j=2:r+1 sum=sum+a(j)*x(i)(