# Numerical Methods for CSE — Teaching Assistance

## Autumn Semester 2016 • D-INFK • ETH Zürich

Welcome to the homepage for my Numerical Methods for CSE teaching assistance at ETH Zürich.

You can find the lecture homepage on which this teaching assistance is based on at https://www.sam.math.ethz.ch/~grsam/HS16/NumCSE/.

## Course Dates

The course takes place on Monday from 10:15 AM to 11:55 AM in the course room ML J34.3.

## Course Lessons

**Lesson 1**26.09.2016

**Topics:**How to use git and GitLab, Eigen3 installation, how to use cmake and make to build the assignment source code, discussion of problem 1.1 and problem 1.2

**Slides:**

- Slides Week 39 PDF

**Lesson 2**28.09.2016

**Topics:**Detailed explanation and derivation of the ${\bf Q}_{j-1}({\bf Q}_{j-1}^T{\bf a}^j)$ approach shown in the solution code of problem 1.2 (Gram-Schmidt orthonormalization with Eigen) using an orthogonal projection ${\bf P}_{Q_{j-1}}$.

**Slides:**

**Lesson 3**03.10.2016

**Topics:**Answers to some questions regarding the exam and exercises in general, presentation of the new workflow for working with the exercise source codek

**Slides:**

- Slides Week 40 PDF

**Lesson 4**10.10.2016

**Topics:**Detailed explanation on how to use cumulative sums for the reutilization of intermediate calculations in the matrix-vector multiplication defined in problem 1.7 (structured matrix–vector product).

**Slides:**

**Lesson 5**10.10.2016

**Topics:**Initializing function parameters and objects in general, how to install MathGL and the Figure class.

**Slides:**

- Slides Week 41 PDF

**Lesson 6**19.10.2016

**Topics:**Some detailed derivations on paper for the problems 2.3 (banded matrix), 2.5 (rank-one perturbations) and 2.6 (Lyapunov equation).

**Slides:**

**Lesson 7**26.10.2016

**Topics:**Some detailed derivations on paper for the problems 2.8 (structured linear systems), 2.9 (triplet ormat to CRS format), 2.12 (grid functions) and 2.13 (efficient sparse matrix-matrix multiplication in COO format).

**Slides:**

**Lesson 8**02.11.2016

**Topics:**Some detailed derivations on paper for the problem 3.1 (matrix least squares in Frobenius norm).

**Slides:**

**Lesson 9**09.11.2016

**Topics:**Some detailed derivations on paper for the problems 3.7 (shape identification) and 3.9 (Cholesky and R decomposition).

**Slides:**

**Lesson 10**15.11.2016

**Topics:**Some detailed derivations on paper for the problems 4.3 (multiplication and division of polynomials based on FFT) and 4.4 (solving triangular Toeplitz systems).

**Slides:**

**Lesson 11**15.11.2016

**Topics:**Some detailed derivations on paper for the problems 5.1 (evaluating the derivatives of interpolating olynomials), 5.3 (Lagrange interpolant) and 5.4 (generalized Lagrange polynomials for Hermite interpolation).

**Slides:**

**Lesson 12**12.12.2016

**Topics:**Some detailed derivations on paper for the problem 8.5 (the order of convergence of an iterative cheme).

**Slides:**

**Lesson 13**12.12.2016

**Topics:**Some detailed derivations on paper for last year's endterm exam (Autumn Semester 2015)