lec11_10022006

# lec11_10022006 - 10.34 Numerical Methods Applied to...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 10.34, Numerical Methods Applied to Chemical Engineering Professor William H. Green Lecture #11: Numerical Calculation of Eigenvalues and Eigenvectors. Singular Value Decomposition (SVD). Singular Value Decomposition (SVD) How do you handle poorly conditioned matrices? A ·x = b What are corresponding eigenvalues for rectangular matrix? ( ) ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ A A or eigenvalues? eigenvectors? Lots of equations and not many unknowns Î rectangular matrix [ ] ∑ ∫ = = ℜ = − ) ( ) , ( ) ( ) ( ) ( ) ( ˆ x c c x f dx x x a x q x f O n n n φ infinite number of equations, finite number of c n Another scenario: Determine how plant is operating: You make more measurements than unknowns . A T A : eigenvalues λ : ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ A A A A T T i i λ σ = Å “singular values of A ” small square matrix A = U ·V ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

lec11_10022006 - 10.34 Numerical Methods Applied to...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online