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# Lecture14 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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Engineering Analysis ENG 3420 Fall 2009 Dan C. Marinescu Office: HEC 439 B Office hours: Tu-Th 11:00-12:00

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2 Lecture 14 Lecture 14 Last time: Solving systems of linear equations (Chapter 9) Graphical methods Cramer’s rule Gauss elimination Today: Discussion of pivoting Tri-diagonal system solver Examples Next Time LU Factorization (Chapter 10)
function x= GaussNaive(A,b ) ExA =[A b]; [ m,n ]= size(A ); q= size(b ); if (m~=n) fprintf ('Error: input matrix is not square; n = %3.0f, m=%3.0f \n', n,m ); End if (n~=q) fprintf ('Error: vector b has a different dimension than n; q = %2.0f \n', q); end n1=n+1; for k=1:n-1 for i=k+1:n factor= ExA(i,k)/ExA(k,k ); ExA(i,k:n1)= ExA(i,k:n1)-factor*ExA(k,k:n1); End End x=zeros(n,1); x(n )=ExA(n,n1)/ExA(n,n); for i=n-1:-1:1 x(i ) = (ExA(i,n1)-ExA(i,i+1:n)*x(i+1:n))/ExA(i,i); end

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>> A=[1 1 1 0 0 0 ; 0 -1 0 1 -1 0 ; 0 0 -1 0 0 1 ; 0 0 0 0 1 -1 ; 0 10 -10 0 -15 -5 ; 5 -10 0 -20 0 0] A = 1 1 1 0 0 0 0 -1 0 1 -1 0 0 0 -1 0 0 -1 0 0 0 0 1 -1 0 10 -10 0 -15 -5 5 -10 0 -20 0 0 b = [0 0 0 0 0 200] >> b=b' b = 0 0 0 0 0 200 >> x = GaussNaive(A,b) x = NaN NaN NaN NaN NaN NaN
Pivoting

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Lecture14 - Engineering Analysis ENG 3420 Fall 2009 Dan C...

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