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Lecture 10 Householder Triangularization NLA Reading Group Spring - PowerPoint PPT Presentation

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Lecture 10 Householder Triangularization NLA Reading Group Spring 13 by Onur Gngr Householder and Gram-Schmidt Gram-Schmidt: triangular orthogonalization Householder: orthogonal triangularization Triangularization by Introducing Zeros

  1. Lecture 10 Householder Triangularization NLA Reading Group Spring ’13 by Onur Güngör

  2. Householder and Gram-Schmidt Gram-Schmidt: triangular orthogonalization Householder: orthogonal triangularization

  3. Triangularization by Introducing Zeros

  4. Householder Reflectors

  5. Householder Reflectors P is the projector onto the space H

  6. Householder Reflectors Instead of We use for numerical stability.

  7. Householder Algorithm

  8. Applying Q This will be employed while solving least squares problems using QR factorization.

  9. Forming Q Q can be formed by calculating Qe 1 , Qe 2 , … and Qe m .

  10. Operation Count Let Each vector requires flops.

  11. Operation Count

  12. Operation Count

  13. Lecture 11 Least Squares Problems NLA Reading Group Spring ’13 by Onur Güngör

  14. Definition

  15. Polynomial Interpolation

  16. Polynomial Least Squares Fitting Solve by minimizing

  17. Orthogonal Projection

  18. Pseudoinverse and Normal Equations

  19. Least Squares via Normal Equations

  20. Least Squares via QR Factorization

  21. Least Squares via SVD

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