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Geometry of Least Squares 2 Least squares from the - PowerPoint PPT Presentation

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1 Geometry of Least Squares 2 Least squares from the perspec0ve of linear algebra (geometry of LSE) Example 3 Line fitting example: 5 y 3 4 3 y 2 2 1 . 6

  1. 1 ¡ Geometry ¡ ¡of ¡Least ¡Squares ¡ ¡ ¡

  2. 2 ¡ Least ¡squares ¡from ¡the ¡ perspec0ve ¡of ¡linear ¡algebra ¡ (geometry ¡of ¡LSE) Example

  3. 3 ¡ Line fitting example: 5 y 3 4 3 y 2 2  1 . 6  ˆ � � x 0 = ( A T A ) − 1 A T y = y 1 1 v ˆ 0 . 26 0 least squares solution 0 1 2 3 4 6 5 t 1 t 3 t 2

  4. 4 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

  5. 5 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

  6. 6 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5

  7. 7 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 >60 3.5

  8. 8 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 >60 3.5

  9. 9 ¡ LS geometry A c 1 A c 2 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 >5 3.5

  10. 10 ¡ Geometry ¡ ¡of ¡Least ¡Squares ¡ ¡ ¡

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