ALAFF Overview

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Subsection 4.1.2 Overview

4.1 Opening
- 4.1.1 Fitting the best line
- 4.1.2 Overview
- 4.1.3 What you will learn
4.2 Solution via the Method of Normal Equations
- 4.2.1 The four fundamental spaces of a matrix
- 4.2.2 The Method of Normal Equations
- 4.2.3 Solving the normal equations
- 4.2.4 Conditioning of the linear least squares problem
- 4.2.5 Why using the Method of Normal Equations could be bad
4.3 Solution via the SVD
- 4.3.1 The SVD and the four fundamental spaces
- 4.3.2 Case 1: $A$ has linearly independent columns
- 4.3.3 Case 2: General case
4.4 Solution via the QR factorization
- 4.4.1 $A$ has linearly independent columns
- 4.4.2 Via Gram-Schmidt QR factorization
- 4.4.3 Via the Householder QR factorization
- 4.4.4 $A$ has linearly dependent columns
4.5 Enrichments
- 4.5.1 Rank Revealing QR (RRQR) via MGS
- 4.5.2 Rank Revealing Householder QR factorization
4.6 Wrap Up
- 4.6.1 Additional homework
- 4.6.2 Summary