arXiv subjects

Pascal den Boef

Publications and source records attributed to Pascal den Boef.

3 recordsLinked to original sources

arXiv2026

Reduced rank extrapolation for multi-term Sylvester equations

We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale problems. For the large-scale problems, an inexact non-stationary iteration is discussed, which makes use of low-rank matrix approximations. Numerical experiments illustrate the potential of the RRE acceleration which often leads to a substantial gain in convergence speed and therefore reducing the consumption of storage and computing time.

math.NA↗

arXiv2025

Generalizing Reduced Rank Extrapolation to Low-Rank Matrix Sequences

Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a fixed-point process for which, generally, the mapping function changes in each iteration. To enable acceleration of the iterative solution for these problems, we propose two novel generalizations of RRE. First, we show how to effectively compute RRE for sequences of low-rank matrices. Second, we derive a formulation of RRE that is suitable for fixed-point processes for which the mapping function changes each iteration. We demonstrate the potential of the methods on several numerical examples involving the iterative solution of large-scale Lyapunov and Riccati matrix equations.

math.NA↗

arXiv2024

Stable Sparse Operator Inference for Nonlinear Structural Dynamics

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.

math.NA↗