lecture31

# lecture31 - IE170 Algorithms in Systems Engineering Lecture...

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Unformatted text preview: IE170: Algorithms in Systems Engineering: Lecture 31 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University April 20, 2007 Jeff Linderoth (Lehigh University) IE170:Lecture 31 Lecture Notes 1 / 14 I Hate A-Rod! Jeff Linderoth (Lehigh University) IE170:Lecture 31 Lecture Notes 2 / 14 And Now You Will Too! Programming Quiz: Monday 1PM A-Rod ruined my day yesterday Therefore, I am going to crush you, just like A-Rod crushes a Joe Borowski hanging slider. Just Kidding Jeff Linderoth (Lehigh University) IE170:Lecture 31 Lecture Notes 3 / 14 LU-Decomposition LU-Decomposition ( A ) 1 n ← rows [ L ] 2 for k ← 1 to n 3 do 4 u kk ← a kk 5 for i ← 1 to n 6 do 7 ik ← a ik /u kk 8 u ki ← a ki 9 for i ← k + 1 to n 10 do 11 for j ← k + 1 to n 12 do 13 a ij ← a ij- ik u kj Jeff Linderoth (Lehigh University) IE170:Lecture 31 Lecture Notes 4 / 14 LU ≈ Gaussian Elimination We either have A = LU or we have MA = U , and L = M- 1 Because of the special structure of M , we have a (fairly) remarkable relationship M- 1 = ( M n- 1 ··· M 2 M 1 )- 1 = M- 1 1 M- 1 2 ··· = L L = 1 m 21 1 m 31 m 32 1 . . . . . . m n 1 m n 2 m n 3 ··· 1 where the m ik are the multipliers from Gaussian elimination! So L and U can be derived directly from the elimination process: ik = m ik = a ( k ) ik a ( k ) kk u kj = a ( k ) kj Jeff Linderoth (Lehigh University) IE170:Lecture 31 Lecture Notes 5 / 14 Recall!...
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lecture31 - IE170 Algorithms in Systems Engineering Lecture...

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