Related papers: Stable and Accurate Interpolation Operators for Hi…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…
A method is presented for forming polynomial interpolants on squares and cubes, which are more efficient in the so-called Euclidean degree than other commonly used methods with the same number of collocation points. These methods have…
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semi-implicit schemes inherit favorable stability properties from the differential inclusion. Their…
We perform stability analyses for discontinuous Galerkin spectral element approximations of linear variable coefficient hyperbolic systems in three dimensional domains with curved elements. Although high order, the precision of the…
In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs)…
In this paper we construct a new H(div)-conforming projection-based p-interpolation operator that assumes only $H^r(K) \cap \tilde H^{-1/2}(div,K)$-regularity (r > 0) on the reference element K (either triangle or square). We show that this…
The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors…
Locality-preserving logical operators in topological codes are naturally fault-tolerant, since they preserve the correctability of local errors. Using a correspondence between such operators and gapped domain walls, we describe a procedure…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
We analyse the interpolation properties of 2D and 3D low order virtual element face and edge spaces, which generalize N\'ed\'elec and Raviart-Thomas polynomials to polygonal-polyhedral meshes. Moreover, we investigate the stability…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Often, such systems arise from the discretization of operator…
Optimizing conversions is crucial in modern online advertising systems, enabling advertisers to deliver relevant products to users and drive business outcomes. However, accurately predicting conversion events remains challenging due to…
We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint operator in a Hilbert space. The algorithm is motivated by a quadrature approximation…
The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the…
We introduce calculus-based formulas for the continuous Euler and homotopy operators. The 1D continuous homotopy operator automates integration by parts on the jet space. Its 3D generalization allows one to invert the total divergence…
This paper examines the stability of the \`a trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…