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lect06

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lect06, Mon 01/28

QR factorization and fitting data by least squares

• Lecture Files

Reading assignment

For Wednesday, read Section 2.9 (norms and condition numbers) of the NCM book.

References for today’s lecture

Sections 5.1, 5.2, and 5.5 of the NCM book.

Outline

Interesting matrices:

• Orthogonal matrices

QR and least squares:

• The factorization A = QR for square matrices A
• Solving Ax = b by QR factorization
• The factorization A = QR for non-square matrices A
• Least squares problems: Ax $\approx$ b
  • a surveying problem
  • parametric curve fitting [next time]
• Solving Ax $\approx$ b by QR factorization [next time]

numpy/scipy routines:

• linalg.qr()
• np.eye()
• npla.lstsq() [next time]
• np.linspace() [next time]