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GAUSS-JORDAN,[object Object],Jorge Eduardo  Celis vargas,[object Object],Code: 2073412,[object Object]
GAUSS-JORDAN,[object Object],Gaussian elimination is an algorithm of linear algebra to determine the solutions of a system of linear equations, matrices and inverse finding.,[object Object],The computational complexity of Gaussian elimination is approximately n3. That is, the number of operations required is n3 if the size of the matrix is n × n,[object Object],Resulting augmented matrix,[object Object],System of linear equations,[object Object]
Mathematical Algorithm,[object Object],Go to the far left column is not zero,[object Object],If the first line has a zero in this column, swap it with another that does not have If,[object Object]
GAUSS-JORDAN,[object Object],Then, get below zero this item forward, adding appropriate multiples of row than the row below it. This is done through the following:,[object Object],Multiply an equation by a nonzero scalar.,[object Object],Exchange of position two equations.,[object Object],Add to a multiple of another equation.,[object Object]
GAUSS-JORDAN,[object Object],Cover the top row and repeat the above process with the remaining ,[object Object],submatrix. Repeat with the rest of the lines (at this point the array is in the form of step),[object Object]
GAUSS-JORDAN,[object Object],Starting with the last line is not zero, move up: for each row get a 1 up front and introduce zero multiples of this sum for the rows corresponding,[object Object],[object Object],[object Object]
Example,[object Object]
Example,[object Object]
Example,[object Object]
Then the solution of this system of equations is: ,[object Object],Example,[object Object]
Flow Chart,[object Object],INICIO,[object Object],i,[object Object],1,[object Object],i=1,n,1,[object Object],j=1,n,1,[object Object],j,[object Object],M(j,i),[object Object],F(i),[object Object]
1,[object Object],k,[object Object],i,[object Object],2,[object Object],j,[object Object],k=i,n,1,[object Object],k=i,n,1,[object Object],j=1,n,1,[object Object],i=1,n,1,[object Object],i=j,[object Object],si,[object Object],no,[object Object],M(j,k)=M(j,k)/M(j,i),[object Object],M(j,k)=M(j,k)-M(j,i)*M(i,k),[object Object],F(j)=F(j)-M(j,i)*F(i),[object Object],F(i)=F(i)/M(j,i),[object Object]
2,[object Object],i,[object Object],j=i-1,1,-1,[object Object],i=n,1,-1,[object Object],k=i,n,1,[object Object],i=1,n,1,[object Object],F(j)=F(j)-M(j,i)*F(i),[object Object],j,[object Object],k,[object Object],M(j,k)=M(j,k)-M(j,i)*M(i,k),[object Object],‘X’(i)=F(i),[object Object],FIN,[object Object]
Code,[object Object],Fortran:,[object Object],programgauss_Jordan,[object Object],integer::i,j,n,k,[object Object],real::a,[object Object],real,allocatable::m(:,:),[object Object],real,allocatable::f(:),[object Object], read(*,*)n,[object Object],allocate(m(n,n),f(n)),[object Object],doi=1,n,1,[object Object],read(*,*)f(i),[object Object], end do,[object Object], doi=1,n,1,[object Object], read(*,*)m(i,1:n),[object Object], end do,[object Object],  do i=1,n,1,[object Object], do j=1,n,1,[object Object], if(i==j)then,[object Object],                a=m(j,i),[object Object], do k=i,n,1,[object Object],                    m(j,k)=(m(j,k))/(a),[object Object],  end do,[object Object],                  f(i)=(f(i))/(a),[object Object],else,[object Object],      a=m(j,i),[object Object], do k=i,n,1,[object Object],      m(j,k)=m(j,k)-a*m(i,k),[object Object],end do,[object Object],      f(j)=f(j)-a*f(i),[object Object],end if,[object Object],end do,[object Object],       end do,[object Object], doi=n,1,-1,[object Object],do j=i-1,1,-1,[object Object],            a=m(j,i),[object Object],do k=j,n,1,[object Object],                m(j,k)=m(j,k)-a*m(i,k),[object Object],end do,[object Object],                f(j)=f(j)-a*f(i),[object Object],end do ,[object Object],                end do,[object Object],doi=1,n,1,[object Object], write(*,*)’x’,(i),’=‘,f(i),[object Object],end do,[object Object],write(*,*)'bn',[object Object], write(*,*)m              ,[object Object],                    close(25),[object Object],end program gauss,[object Object]
[object Object],package javaapplication1;,[object Object],importjavax.swing.JOptionPane;,[object Object],importjava.util.Scanner;,[object Object],publicclassGauss_Jordan {,[object Object],publicstaticvoidmain(String[] args) {,[object Object],inti,j,k,n;,[object Object],double a;,[object Object],double m[][],f[];,[object Object],Scanner reader=new Scanner(System.in);,[object Object],System.out.println("escriba n");,[object Object],n=reader.nextInt();,[object Object],m=new double [n][n];,[object Object],f=new double [n];,[object Object],for(i=0;i<n;i++){,[object Object],    f[i]=Double.parseDouble(JOptionPane.showInputDialog("f"+i));,[object Object],for(j=0;j<n;j++){,[object Object],m[i][j]=Double.parseDouble(JOptionPane.showInputDialog("M("+i+j+")"));}},[object Object],for(i=0;i<n;i++){,[object Object],for(j=0;j<n;j++){,[object Object],        a=m[j][i];,[object Object]
if(i==j){,[object Object],for(k=i;k<=n;k++){,[object Object],                m[j][k]=(m[j][k]/a);},[object Object],        f[i]=(f[i]/a);},[object Object],else {,[object Object],for(k=i;k<=n;k++){,[object Object],                m[j][k]=m[j][k]-a*m[i][k];},[object Object],        f[j]=f[j]-a*f[i];}}},[object Object],for(i=n;i>=0;i--){,[object Object],for(j=i-1;j>=0;j--){,[object Object],        a=m[j][i];,[object Object],for(k=j;k<=n;k++){,[object Object],           m[j][k]=m[j][k]-a*m[i][k];},[object Object],    f[j]=f[j]-a*f[i];}},[object Object],for(i=0;i<n;i++){,[object Object],System.out.println("x"+i+"="+f[i]);}}},[object Object]
bibliography,[object Object],http://www.acatlan.unam.mx/acatlecas/mn/sistemas.htm#3.1.1._Método_de_Gauss_,[object Object],Internet wikipedia.,[object Object]
Gauss jordan

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Gauss jordan

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