# Teaching

# Seminar numerical analysis

Gaps in the bachelor-master program in numerically oriented research topics in the widest sense are being dealt with in this seminar, as well as topics relating to the theses of the participating students. The seminar format aims at a balance between presentations by the participating students and the responsible research groups.

Several guest speakers will also be invited.

## Practical information

Students |
Master of Mathematics: Financial Mathematics (part 1 or 2) |

Period |
1st/2nd term 2016-2017 |

Contact hours |
Monday 16.00-18.00, room M.G.016check the time schedule for the right dates and times |

Tutors |
prof. dr. Annie Cuyt prof. dr. Karel in 't Hout prof. dr. Wim Vanroose prof. dr. Uwe Peter Wystup |

## Time schedule

**3 October 2016 — Introduction**

**10 October 2016 — Sparse interpolation (part 1)**

Tutorial by Annie CuytThroughout computational science and engineering, several attempts have been made to represent data in a parsimonious way. Mathematical models are proposed in which the major features of the data are represented using only a few terms, in other words, models that use a sparse combination of generating elements instead of a linear combination of all basis elements. Besides the accuracy of a representation, its sparsity has gradually become a priority. This is because a sparser model means higher compression, less data collection, storage or transmission, and a reduced model complexity.

A representation is called t-sparse if it is a combination of only t elements. In sparse interpolation, the aim is to determine both the support of the sparse linear combination and the scalar coefficients in the representation, from a small or minimal amount of data samples. Sparse techniques solve the problem statement from a number of samples proportional to the number t of terms in the representation rather than the number of available data points or available generating elements.

We indicate the connections between sparse interpolation, coding theory, generalized eigenvalue computation, exponential analysis and rational approximation. In the past few years, insight gained from the computer algebra community combined with methods developed by the numerical analysis community, has lead to significant progress in several very practical and real-life signal processing applications. We make use of tools such as the singular value decomposition and various convergence results for Padé approximants to regularize an otherwise inverse problem. Classical resolution limitations in signal processing with respect to frequency and decay rates, are overcome.

In the illustrations we particularly focus on multi-exponential models representing signals which fall exponentially with time. These models appear, for instance, in transient detection, motor fault diagnosis, electrophysiology, magnetic resonance and infrared spectroscopy, vibration analysis, seismic data analysis, music signal processing, dynamic spectrum management such as in cognitive radio, nuclear science, and so on.

Files:exp.mw, poly.mw, ExpLog.txt, RevChRem.txt.

**17 October 2016 — Sparse interpolation (part 2)**

Tutorial by Annie Cuyt

**24 October 2016 — Low-rank matrix approximation**

Talk by Ivan Markovsky (Vrije Universiteit Brussel)State-of-the-art data processing methods are model based and require a model identification step prior to solving the data processing problem. Starting with a review of classical system identification, this talk presents a model-free data processing approach, in which model parameters need not be explicitly estimated. The underlying computational tool in the new setting is low-rank approximation of a structured matrix constructed from the data. Preserving the structure in the approximation leads to statistically optimal estimators as well as to fast computational methods.

Slides:Low-rank approximation problems in system identification, Structured low-rank approximation approach to sum-of-exponentials

**21 November 2016 — Introduction to tensor decompositions**

Talk by Mariya Ishteva (Vrije Universiteit Brussel)

**30 November 2016**

Presentation by Gitte Bluekens

Presentation by Elise Kuylen

**5 December 2016 — Computational models for diffusion MRI**

Talk by Ben Jeurissen (Universiteit Antwerpen)

**12 December 2016**

Presentation by Geertje Van Hove

Presentation by Ward Demyttenaere

**23 December 2016**

Presentation by Wannes Naudts

Presentation by Ferre Knaepkens

## Project subjects

- Geertje Van Hove : Padé Laplace method
- Wannes Naudts : Variable projection method
- Ward Demyttenaere : Waring decomposition
- Ferre Knaepkens : Blind source separation

## Extra

Spreken voor een volle zaal (Bob de Groof)