review2.dvi
ECS130 Midterm II Review Checklist
1. Polynomial interpolation
• Polynomial interpolation in power form
• Polynomial interpolation in Lagrange form
• Piecewise linear interpolation (= linear spline)
2. Least squares and curve fitting
Least-squares problem: minβ ‖Xβ − y‖2
• Normal equation (XTX)β = XT y
• QR method
Tools of trade:
• Householder reflection H = I − ρuuT
• The QR factorization: A = QR
• Pseudoinverse
Curve fitting:
• model
• design matrix and parameters β
3. Eigenvalues and singular values
• Eigenvalue and eigenvector definition
• Eigenvalue decomposition: A = XDX−1
• Singular value and singular vector definition
• Singular value decomposition (SVD): A = UΣV T
• Relationship between eigenvalues/vectors and singular values/vectors
• The power method and inverse iteration
• Applications of SVD
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