Related papers: Exploiting variable precision in GMRES
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…
In this work, we propose an adaptive spectral element algorithm for solving nonlinear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer-Gauss points combined with very accurate and stable…
In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of…
The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data…
In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation.In a recent article, we obtained promising…
Aitken extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition…
Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This…
We discuss the application of the Discrete Variable Representation to Schr\"odinger problems which involve singular Hamiltonians. Unlike recent authors who invoke transformations to rid the eigenvalue equation of singularities at the cost…
Gaussian Processes (GPs) are powerful kernelized methods for non-parameteric regression used in many applications. However, their use is limited to a few thousand of training samples due to their cubic time complexity. In order to scale GPs…
Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
$H^1$-conforming Galerkin methods on polygonal meshes such as VEM, BEM-FEM and Trefftz-FEM employ local finite element functions that are implicitly defined as solutions of Poisson problems having polynomial source and boundary data.…
Since many years ago, multilateration has been used in precision engineering notably in machine tool and coordinate measuring machine calibration. This technique needs, first, the use of laser trackers or tracking interferometers, and…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the…
To investigate solutions of (near-)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discrete-time systems. Assuming the plant dynamics is homogeneous, we first derive a scaling…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput.,…
We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the…