251 Lecture 10 Householder

251 Lecture 10 Householder - Householder Triangularization...

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Click to edit Master subtitle style 4/14/11 Householder Triangularization Do you remember the projection P = I – aa*/a*a ?
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Click to edit Master subtitle style 4/14/11 Householder Triangularization Do you remember the projection (Lecture 6) P = I – aa*/a*a ? Projects along a to orthogonal plane H H a
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Click to edit Master subtitle style 4/14/11 Householder Triangularization What can you say about this matrix (familiar)? 1/r11 - r12/r1 1 - r13/r1 1 1 1
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Click to edit Master subtitle style 4/14/11 Householder Triangularization And this matrix (familiar)? 1/r11 - r12/r1 1 - r13/r1 1 1 1 1 1/r22 - r23/r2 2 1
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Click to edit Master subtitle style 4/14/11 Householder Triangularization Final matrix? 1/r11 - r12/r1 1 - r13/r1 1 1 1 1 1/r22 - r23/r2 2 1
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Click to edit Master subtitle style 4/14/11 Gram-Schmidt! qi = ( ai - Σj=1,m rijqi-1) / rii where rij = q*iaj for i ≠ j and rii = lengths A = QR = Q R1R2 … Rn where Ri = 1/rii
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Click to edit Master subtitle style 4/14/11 Householder Triangularization Look for matrices Q1Q2 … Qn so that Q1Q2 … Qn A = R or (since Q1Q2 … Qn are unitary) A = QR = Q1*Q2* … Qn* R
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251 Lecture 10 Householder - Householder Triangularization...

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