This course provides a first introduction to the field of numerical analysis with a strong focus on visual computing and machine learning applications. Using examples from computer graphics, deep neural networks, geometry processing, computer vision, and computational photography, students will gain hands-on experience with a range of essential numerical algorithms.
The course will begin with a review of floating point arithmetic and error propagation in numerical computations. Following this, we will study and experiment with several techniques that solve systems of linear and non-linear equations and perform dimensionality reduction. Since many interesting problems cannot be solved exactly, numerical optimization techniques constitute the second major topic of this course. We will take an extensive look at automatic differentiation, the mechanism underlying popular deep learning frameworks such as PyTorch and Tensorflow. The course concludes with a review of numerical methods that introduce randomness to solve problems that would otherwise be intractable.
Students will have the opportunity to gain practical experience with the discussed methods using programming assignments based on Scientific Python.