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lect07

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lect07, Wed 01/30

Least squares; matrix condition number and norm

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Reading assignment

For next Monday, read Section 1.7 (floating-point arithmetic) of the NCM book, and look at this Wikipedia page on floating-point format.

References for today’s lecture

Section 2.9 (norms and condition numbers) of the NCM book.

Outline

Finishing up QR and least squares:

• Solving Ax $\approx$ b by QR factorization
• Parametric curve fitting

Norm and condition number:

• Norm of a vector: l_2 (Euclidean) norm and others
• Condition number of a matrix [next time]
• Sensitivity analysis of Ax = b [next time]
• Norm of a matrix [next time]

numpy/scipy routines:

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

several matplotlib routines, see in-class transcript