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Hu Weifei Master’s Degree Dept. of Mechanical Engineering Hanyang University

Presentation-HW#2 -1. Hu Weifei Master’s Degree Dept. of Mechanical Engineering Hanyang University. Review. Perturbation. In system Ax = b , the change of solution caused by “small” change (perturbation) in A and b. Perturbation on A. Perturbation on A and b.

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Hu Weifei Master’s Degree Dept. of Mechanical Engineering Hanyang University

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  1. Presentation-HW#2 -1 Hu Weifei Master’s Degree Dept. of Mechanical Engineering Hanyang University

  2. Review Perturbation In system Ax=b, the change of solution caused by “small” change (perturbation) in A and b. Perturbation on A Perturbation on A and b Problem 1 belong to category of perturbation on A and b.

  3. Review Perturbation on A

  4. Review Perturbation on A and b Conclusion: Problem 1 belong to category of perturbation on A and b, and we will justify this conclusion.

  5. Solution Define A, s, b, the solution Ax=b is clearly s.

  6. Solution Perturb the system slightly

  7. Solution

  8. Solution The perturbation in solution, A and b are dx, dA and db, respectively Compare dx, dA and db, the sizes are similar

  9. Solution Calculate ?? Check our hypothesis ?? The condition number is appropriately small Well-conditioned This value is large smaller than 1 Well satisfied

  10. Solution Using Matlab to solve the left-hand-side of above inequality Using Matlab to solve the right-hand-side of above inequality CONCLUDE: LHS < RHS

  11. Solution Repeat the perturbation analysis t=1.0e-04 The condition number is appropriately small, well-conditioned This value is large smaller than 1, well satisfied CONCLUDE: LHS < RHS

  12. Solution Repeat the perturbation analysis t=1.0e-02 The condition number is appropriately small, well-conditioned This value is large smaller than 1, well satisfied CONCLUDE: LHS < RHS

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