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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\rm cosh} x} using your minimizer. Do you get the expected result?
