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Randomized orthogonal projection methods (ROPMs) can be used to speed up the computation of Krylov subspace methods in various contexts. Through a theoretical and numerical investigation, we establish that these methods produce…

We devise and analyze a reduced basis model order reduction (MOR) strategy for an abstract wave problem with vanishing initial conditions and a source term given by the product of a temporal Ricker wavelet and a spatial profile. Such wave…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of…

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real-time. Simultaneously we observe an increase in model sophistication on the one hand and growing demands on the quality of risk…

Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…

In this paper we construct Ritz-type projectors with boundary interpolation properties in finite dimensional subspaces of the usual Sobolev space and we provide a priori error estimates for them. The abstract analysis is exemplified by…

Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary data distributions i.e. they generalize…

We prove that directional wavelet projections and Riesz transforms are related by interpolatory estimates. The exponents of interpolation depend on the H\"older estimates of the wavelet system. This paper complements and continues previous…

Inspired by the works of Forman on discrete Morse theory, which is a combinatorial adaptation to cell complexes of classical Morse theory on manifolds, we introduce a discrete analogue of the stratified Morse theory of Goresky and…

We consider a Krylov subspace approximation method for the symmetric differential Riccati equation $\dot{X} = AX + XA^T + Q - XSX$, $X(0)=X_0$. The method we consider is based on projecting the large scale equation onto a Krylov subspace…

In this paper we prove an optimal error estimate for the H(curl)-conforming projection based p-interpolation operator introduced in [L. Demkowicz and I. Babuska, p interpolation error estimates for edge finite elements of variable order in…

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far…

In convergence analysis of finite element methods for singularly perturbed reaction--diffusion problems, balanced norms have been successfully introduced to replace standard energy norms so that layers can be captured. In this article, we…

In this paper, we investigate Gaussian process regression models where inputs are subject to measurement error. In spatial statistics, input measurement errors occur when the geographical locations of observed data are not known exactly.…

We generalize two-point interpolatory Hermite quadrature to functions with available values and the first (n-1) derivatives at both end points. Armed with integration by parts in the reverse form we provide an elementary derivation of an…

Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…

In this paper we present a new family of rules for numerical integration. This family has up to half the error of the widely used Newton-Cotes rules when a sufficient number of points is evaluated and also much better numerical stability…

Shuffling gradient methods are widely used in modern machine learning tasks and include three popular implementations: Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG). Compared to the empirical success, the…

Morphing is a long-standing problem in vision and computer graphics, requiring a time-dependent warping for feature alignment and a blending for smooth interpolation. Recently, multilayer perceptrons (MLPs) have been explored as implicit…