251 Lecture 10 Householder

# 251 Lecture 10 Householder - Householder Triangularization...

This preview shows pages 1–8. Sign up to view the full content.

Click to edit Master subtitle style 4/14/11 Householder Triangularization Do you remember the projection P = I – aa*/a*a ?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/13/2011 for the course CSCE 211 taught by Professor Staff during the Spring '08 term at Columbia SC.

### Page1 / 19

251 Lecture 10 Householder - Householder Triangularization...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online