Numerical Analysis

The Society for Industrial and Applied Mathematics convenes its triennial conference on applied and numerical linear algebra. The programme covers matrix computations, machine learning, quantum simulation, inverse problems, high-performance computing, dynamical systems, model reduction, optimal transport, network science, tensor methods and related applications. Proposal submissions are currently…

Yousef Saad examines relaxed gradient descent for large-scale optimization. Relaxing the optimal step length in Cauchy's steepest descent avoids its characteristic zigzag behavior and can bring the search direction close to an eigenvector of the Hessian. Once that alignment is sufficiently accurate, properties of the Lanczos method can accelerate convergence. The talk analyzes several such…

Matthias Bolten discusses the scalability of multigrid solvers for linear systems arising from discretized partial differential equations. On modern supercomputers, heterogeneous CPUs and GPUs and the widening gap between computation, network, and memory speeds complicate parallelization. Classical multigrid analysis relies on tightly coupled multiplicative components, whereas additive and…

Vasileios Kalantzis develops iterative linear algebra algorithms that tolerate incomplete matrix-vector products in controller-worker cloud systems. Richardson and Chebyshev schemes solve linear systems using randomly available product entries, replacing missing entries with zero. For dominant eigenvectors, modified power iterations substitute zeros, previous entries, or averages of partial…

Doctoral research on energy-variational solutions of hyperbolic conservation laws in fluid mechanics. The project studies existence for deterministic and stochastic PDEs and numerical approximation schemes, with Robert Lasarzik and Thomas Eiter. The initial appointment is three years at 75% employment (29.25 hours weekly), TVöD Bund E13. Mobile working is available. Applications remain open until filled; the first assessment was planned for 14 September 2026. Apply through the employer portal with a motivation letter, CV, certificates, MSc course grades and thesis or current draft.

Carry out independent and collaborative research in numerical analysis, machine learning, statistical inference, computational biophysics or scientific computing at the Center for Computational Mathematics. Fellows receive mentoring, computing resources and a travel/research budget, contribute to publications and potentially open-source software, and may mentor summer students. Appointments initially last two years and may be renewed for a third based on performance. The anticipated start is July–October 2027. This is a New York City onsite position allowing one day per week working from home. Annual full-time compensation is $95,000, with benefits and possible subsidised housing. Review begins in late autumn 2026 and continues until filled; applications and references received by 15 November 2026 receive full consideration.

Misha Kilmer develops structured matrix approximation by an invertible matrix-to-tensor transformation, tensor approximation, and a mapping back to matrix space. Different tensor decompositions yield sums of structured Kronecker products, block low-rank matrices, or combinations of both. The framework exposes latent operator structure useful for large computations, and the talk considers where…