Multivariate rational functions with applications

The PhD will be carried out in the NUMA research section of the Department of Computer Science at KU Leuven. The research at NUMA covers a broad area of numerical analysis, applied mathematics and scientific computing.
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Project

Polynomials are ubiquitous in analysis and scientific computing, while rational functions are equally foundational but relatively unexplored in comparison. Advances in the past five to ten years have resulted in great strides forward both in numerical tools and in applicability of rational functions of a single variable. It is the goal of the project to make another leap forward, by building tools for rational functions of several variables. Solving the strongly nonlinear problem of best approximation using multivariate rational functions is highly challenging and would be transformative across disciplines. The project identifies several paths towards that ambitious goal, each within the joined expertise of the PIs, with progressive levels of complexity. Specific research goals focus on the numerical representation of rational functions, on numerical algorithms to solve nonlinear rational approximation problems, and on applications in model order reduction and (nonlinear) eigenvalue problems.

Profile

The candidate holds a master degree in mathematics or mathematical engineering or equivalent programme, is interested in mathematical research in an academic environment and aims for obtaining a PhD degree.

Offer

NUMA is an ambitious and vibrant research section, that covers many fields of numerical analysis, numerical algorithms and applications. NUMA is one of the largest numerical groups in Europe. The initial offer is a scholarship for a period of one year, which will, after positive evaluation, be extended to four years. The researcher will work in the NUMA research section among 40 other researchers working on a variety of numerical topics. The researcher will also contribute to the didactical tasks of the NUMA section.

Interested?

For more information please contact Prof. dr. ir. Daan Huybrechs, tel.: +32 16 32 70 58, mail: [email protected] or Prof. dr. ir. Karl Meerbergen, tel.: +32 16 32 79 59, mail: [email protected].

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