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function [x]= solsup(U,b) [n,m]=size(U); x=zeros(n,1); if abs(U(n,n))<%eps

function [x]= solsup(U,b) [n,m]=size(U); x=zeros(n,1); if abs(U(n,n))<%eps error('un pivot de Gauss n''est pas défini'); end x(n)=b(n)/U(n,n); for i=n-1:-1:1 if abs(U(i,i))<%eps error('un pivot de Gauss n''est pas défini'); end x(i)=(b(i)-U(i,i+1:n)*x(i+1:n))/U(i,i);

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function [x]= solsup(U,b) [n,m]=size(U); x=zeros(n,1); if abs(U(n,n))<%eps

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  1. function [x]= solsup(U,b) [n,m]=size(U); x=zeros(n,1); if abs(U(n,n))<%eps error('un pivot de Gauss n''est pas défini'); end x(n)=b(n)/U(n,n); for i=n-1:-1:1 if abs(U(i,i))<%eps error('un pivot de Gauss n''est pas défini'); end x(i)=(b(i)-U(i,i+1:n)*x(i+1:n))/U(i,i); end endfunction function [U,e]=trisup(A,b) [n,m]=size(A); U=A; e=b; for k=1:n-1 if abs(U(k,k))<%eps error('pivot nul'); else for i=k+1:n c=U(i,k)/U(k,k); e(i)=e(i)-c*e(k); U(i,k)=0; U(i,k+1:n)=U(i,k+1:n)-c*U(k,k+1:n); end end end if abs(U(n,n))<%eps error('pivot nul'); endfunction

  2. function [x] = resolG(A,b) getf trisup.sci getf solsup.sci [U,e]=trisup(A,b); x=solsup(U,e); endfunction function [L,U]=LU(A) [n,m]=size(A); L=eye(n,n); U=A; for k=1:n-1 if abs(U(k,k))<%eps error('pivot nul'); else for i=k+1:n c=U(i,k)/U(k,k); U(i,k)=0; L(i,k)=c; U(i,k+1:n)=U(i,k+1:n)-c*U(k,k+1:n); end end end if abs(U(n,n))<%eps error('pivot nul'); end endfunction

  3. function [x]= solinf(U,b) [n,m]=size(U); x=zeros(n,1); if abs(U(1,1))<%eps error('un pivot de Gauss n''est pas défini'); end x(1)=b(1)/U(1,1); for i=2:n if abs(U(i,i))<%eps error('un pivot de Gauss n''est pas défini'); end x(i)=(b(i)-U(i,1:i-1)*x(1:i-1))/U(i,i); end endfunction function [x]= resolLU(A,b) getf LU.sci getf solinf.sci getf solsup.sci [L,U]=LU(A); y=solinf(L,b); x=solsup(U,y); endfunction

  4. function [B]= inverse(A) getf reslLU.sci; [u v]=size(A); B=zeros(u,u); I=eye(u,u); for i=1:u B(1:u,i)=resolLU(A,I(1:u,i)); end endfunction

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