程序代写代做代考 review2.dvi

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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