Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

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For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

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The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

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We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

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Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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Randomized low-rank approximation and its applications

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Randomized flexible GMRES with deflated restarting

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Spectral Estimators for High-Dimensional Matrix Inference

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

The time-domain Cartesian multipole expansion of electromagnetic fields

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Reliable data-driven decision-making through optimal transport

Accelerator-driven Data Arrangement to Minimize Transformers Run-time on Multi-core Architectures

Aerodynamic modeling of a delta-wing UAV for model-based navigation

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Orbital-Resolved DFT plus U for Molecules and Solids

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

Preconditioning techniques for generalized Sylvester matrix equations

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems