Giuseppe Accaputo

Numerical Methods for CSE Exercise Sessions
D-MATH • ETH Zürich • Autumn Semester 2016

Numerical Methods for CSE Exercise Sessions (D-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

Content: Some detailed derivations on paper for last year's endterm exam (Autumn Semester 2015)
Content: Some detailed derivations on paper for the problem 8.5 (the order of convergence of an iterative scheme).
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).
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).
Content: Some detailed derivations on paper for the problems 3.7 (shape identification) and 3.9 (Cholesky and QR decomposition).
Content: Some detailed derivations on paper for the problem 3.1 (matrix least squares in Frobenius norm).
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).
Content: Some detailed derivations on paper for the problems 2.3 (banded matrix), 2.5 (rank-one perturbations) and 2.6 (Lyapunov equation).
Content: Initializing function parameters and objects in general, how to install MathGL and the Figure class.

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).

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

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

Source code: Gram-Schmidt algorithm implementation using two for-loops (.cpp • 1.6 kB)

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