Subsection 3.1.2 Overview Week 3
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3.1 Opening Remarks
3.1.1 Choosing the right basis
3.1.2 Overview Week 3
3.1.3 What you will learn
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3.2 3.2 Gram-Schmidt Orthogonalization
3.2.1 Classical Gram-Schmidt (CGS)
3.2.2 Gram-Schmidt and the QR factorization
3.2.3 Classical Gram-Schmidt algorithm
3.2.4 Modified Gram-Schmidt (MGS)
3.2.5 In practice, MGS is more accurate
3.2.6 Cost of Gram-Schmidt algorithms
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3.3 Householder QR Factorization
3.3.1 Using unitary matrices
3.3.2 Householder transformation
3.3.3 Practical computation of the Householder vector
3.3.4 Householder QR factorization algorithm
3.3.5 Forming Q
3.3.6 Applying QH
3.3.7 Orthogonality of resulting Q
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3.4 Enrichments
3.4.1 Blocked Householder QR factorization
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3.5 Wrap Up
3.5.1 Additional homework
3.5.2 Summary