Unit 3 · Orthogonality and Least Squares

Chapter 3.2

Least Squares

When Ax = b has no solution, solve the nearest problem that does: project b where it can be reached. Fitting a line to data is exactly this.

12–16 min · in preparation · lesson 10 of 21

By the end

  1. 01Derive the normal equations AᵀAx̂ = Aᵀb
  2. 02Fit lines and curves to data by least squares
  3. 03Interpret the residual as the unreachable component of b

In unit 3

  1. 3.1Orthogonality and Projections12–16
  2. 3.2Least Squares12–16
  3. 3.3Gram-Schmidt and A = QR11–15
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