# Numerical Methods for CSE Exercise SessionsD-MATH • ETH Zürich • Autumn Semester 2016

Welcome to the homepage for the Numerical Methods for CSE (D-MATH) exercise sessions given by Giuseppe Accaputo, where you can download the slides (and other course material) for each exercise session in PDF format. The official lecture homepage for this course can be found at https://www.sam.math.ethz.ch/~grsam/HS16/NumCSE/.

## Course Information

The exercise session takes place every Monday from 10:15 AM to 11:55 AM in the room ML J34.3.

On September 26 and October 3 I will be present at the Study Center in the room HG E41 from 18:00 PM to 20:00 PM.

## Exercise Sessions

w51

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

w50

Content: Some detailed derivations on paper for the problem 8.5 (the order of convergence of an iterative scheme).

w47

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

w46

Content: 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).

w45

Content: Some detailed derivations on paper for the problems 3.7 (shape identification) and 3.9 (Cholesky and QR decomposition).

w44

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

w43

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

w42

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

w41

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

W41

Content: 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).

w40

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

W39

Content: 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 ${\bf P}_{Q_{j-1}}$.

W39

Content: 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