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# Lecture Notes

On this page, we collect Lecture Notes that we have created in the context of ML2R and other teaching activities.

## ML2R Coding Nuggets

1. Solving Linear Programming Problems by Pascal Welke and Christian Bauckhage.

This note discusses how to solve linear programming problems with SciPy. As a practical use case, we consider the task of computing the Chebyshev center of a bounded convex polytope.

2. Linear Programming for Robust Regression by Pascal Welke and Christian Bauckhage.

Having previously discussed how scipy allows us to solve linear programs, we can study further applications of linear programming. Here, we consider least absolute deviation regression and solve a simple parameter estimation problem deliberately chosen to expose potential pitfalls in using scipy's optimization functions.

3. Numerically Solving the Schrödinger Equation (Part 1) by Christian Bauckhage.

Most quantum mechanical systems cannot be solved analytically and therefore require numerical solution strategies. In this note, we consider a simple such strategy and discretize the Schrödinger equation that governs the behavior of a one-dimensional quantum harmonic oscillator. This leads to an eigenvalue / eigenvector prob- lem over finite matrices and vectors which we then implement and solve using standard NumPy functions.

4. Numerically Solving the Schrödinger Equation (Part 2) by Christian Bauckhage.

We revisit the problem of numerically solving the Schrödinger equation for a one-dimensional quantum harmonic oscillator. We reconsider our previous finite difference scheme and discuss how higher order finite differences can lead to more accurate solutions. In particular, we will consider a five point stencil to approximate second order derivatives and implement the approach using SciPy functions for sparse matrices.

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