Physics 212, 2017: Lecture 14

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Back to Physics 212, 2017: Computational Modeling.

Why is fitting hard: Large dimensionality, multiple minima, flat regions. What is the maximum accuracy of optimization?

For future lectures, start reading:

• http://docs.scipy.org/doc/scipy/reference/optimize.html -- Optimization with Python/SciPy

In the class lectures for this module, we will talk about the following methods:

• Multi-dimensional linear regression (no derivations) using numpy.linalg.lstsq http://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.linalg.lstsq.html
• General considerations for nonlinear minimization (with and without derivatives; with and without second derivatives)
• Golden mean 1-d search
• Parabolic interpolation
• Newton method

Your turn

Write down a parabolic interpolation or Newton method minimizer of 1-d functions. Minimize a ${\rm {cosh}}x$ using your minimizer. Do you get the expected result?

• Submit your work.