Algorithms for eigenvalue problems with eigenvector nonlinearity.

Algorithms for eigenvalue problems with eigenvector nonlinearity.

The Numerical Analysis & Applied Mathematics (NUMA) section of KU Leuven counts 19 Faculty members. It has a long tradition of analysis and development of numerical methods for a large variety of problems. The research topics include numerical (multi)-linear algebra, computational algebraic geometry, approximation theory, uncertainty quantification, numerical simulation, control and optimization, numerical methods for data science and numerical software. The section collaborates with many research teams of the Faculties of Engineering Science and Engineering Technology, with groups in the Departments of Mathematics and of Physics in Leuven, and with other teams in Belgium and abroad.

KU Leuven is one of the world’s leading universities, ranking #46 in the Times Higher Education World University Rankings 2026. It is also among Europe’s most successful universities in competitive European research funding, ranking first among higher education institutions in Horizon Europe and the Marie Skłodowska-Curie Actions program. It offers an exciting multidisciplinary research environment, many opportunities for collaboration, and a broad range of training courses.

Nonlinear eigenvalue problems with eigenvector nonlinearities are algebraic eigenvalue problems whose matrix depends on the eigenvector itself. Applications arise in areas ranging from electronic structure computations to machine learning.

This class of eigenvalue problems is particularly challenging because of its inherent nonlinearity, while the concept of linearization, in the sense of an equivalent, possibly infinite-dimensional linear representation, remains elusive. Consequently, the underlying theory is still incomplete, and available numerical methods rely almost exclusively on fixed-point iterations whose global convergence properties are understood only in specific settings. At the same time, the relevant literature is rather limited and dispersed across different research domains.

The aim of the postdoc position is to strengthen a research project within NUMA on structure-exploiting algorithms for eigenvector nonlinearities with a strong theoretical foundation. The first objective of this project is the construction of multivariable rational approximations that give rise to spectrally equivalent linear problems; second, the development of global algorithms that can reliably compute all eigenvalues within a prescribed region or interval; third, the use of projection-based techniques to extend these algorithms to large-scale problems, thereby bridging the gap between methodological developments and practical applications.

The proposed methodology combines techniques from rational approximation, multi-parameter eigenvalue algorithms, and nonlinear algebra, while leveraging the complementary expertise of the advisors, Karl Meerbergen and Wim Michiels. The research team, comprising the advisors and a doctoral student, is embedded in a strong network of international collaborations.

Profile

The ideal candidate has a PhD degree in mathematics (applied, computational mathematics) or Engineering (Mechanical, Electrical, Mathematical Engineering) with key experience in the domain adjacent to the project.

Offer

We offer
a fully funded postdoc position in an international context one year at the Numerical Analysis and Applied Mathematics (NUMA) research unit of KU Leuven, a hub for interdisciplinary research in the field of Computational and Applied Mathematics.
The funding includes a very competitive tax-free scholarship as well as social and medical insurance.

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location_city Locatie: Leuven