Nonlinear eigenvalue problems with eigenvector nonlinearities

27 Jan 2024
Job Information

Organisation/Company

KU Leuven

Research Field

Computer science

Researcher Profile

First Stage Researcher (R1)

Country

Belgium

Application Deadline

15 Feb 2024 - 00:00 (UTC)

Type of Contract

Temporary

Job Status

Full-time

Hours Per Week

38 hours/week

Is the job funded through the EU Research Framework Programme?

Not funded by an EU programme

Reference Number

BAP-2024-50

Is the Job related to staff position within a Research Infrastructure?

No

Offer Description

Nonlinear eigenvalue problems with eigenvector nonlinearities are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from electron structure computations to machine learning. This class of eigenvalue problems is challenging as they are inherently nonlinear while the concept of linearization, in the sense of an equivalent, possibly infinite-dimensional linear representation, is not clear. As a consequence, the basis theory is incomplete, while the available algorithms almost exclusively rely on a fixed point iteration whose global convergence properties are only understood in specific cases. At the same time, the literature is limited and scattered over different domains.

The aim of the PhD is to develop structure exploiting algorithms for eigenvector nonlinearities with strong theoretical foundations. First, multivariable rational approximations will be constructed that induce spectrally equivalent linear problems. Second, global algorithms will be developed, able to reliably compute all eigenvalues in a prescribed region or interval. Third, using projection these algorithms will be scaled up to large-scale matrices, which is essential to bridge methods andapplications.
The methodology integrates techniques from rational approximation, algorithms for multi-parameter eigenvalues and methods from algebraic geometry. The PhD project fits within a longstanding collaboration of the research groups of the PhD advisors K. Meerbergen and W. Michiels. As part of the PhD project, a two-month research stay at the Max Planck institute for Mathematics in the Sciences in Leipzig is foreseen.

Requirements

Research Field

Engineering

Education Level

Master Degree or equivalent

Languages

ENGLISH

Level

Good

Additional Information
Benefits

We offer fully funded PhD position in an international context for four years at the Numerical Analysis and Applied Mathematics (NUMA) section of KU Leuven, a top European university and hub for interdisciplinary research in computational mathematics and mathematical engineering. The targeted starting date is in fall 2023 (the exact starting date is to be discussed).

Eligibility criteria

The ideal candidate has a Master degree in  mathematical engineering or applied mathematics. 

Selection process

Vul contactpersonen aan in stap 1 "Context vacature" en hergenereer deze tekst.
You can apply for this job no later than 15/02/2024 via the online application tool

Work Location(s)

Number of offers available

1

Company/Institute

KU Leuven

Country

Belgium

State/Province

Vlaams Brabant

City

Leuven

Postal Code

3000

Street

Leuven

Geofield

Where to apply

Website

https://easyapply.jobs/r/ikuat9i21ecrhi2KXa4I

Contact

State/Province

Leuven

City

Vlaams Brabant

Street

Leuven

Postal Code

3000

STATUS: EXPIRED