Related papers: Error bounds for spectral enhancement which are ba…
In conventional spectral/finite element methods, the triangulation/quadrilateralization of the domain produces many interior edges which require additional DOF. What if we could directly use the original hull without going to…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
In the present article we study strong approximation of solutions of scalar stochastic differential equations (SDEs) with bounded and $\alpha$-H\"older continuous drift coefficient and constant diffusion coefficient at time point $1$.…
In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral…
Classification models are expected to perform equally well for different classes, yet in practice, there are often large gaps in their performance. This issue of class bias is widely studied in cases of datasets with sample imbalance, but…
The construction of computer models (mathematical models implemented in computer codes), with respect to observed phenomena, is usually undertaken by building different variants depending on modeller sensibility, and choosing the one…
Simple upper and lower bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-\frac{1}{2}$, $0<\gamma<1$. Most of our bounds for this integral are tight as $x\rightarrow\infty$. We…
This investigation is motivated by PDE-constrained optimization problems arising in connection with electrocardiograms (ECGs) and electroencephalography (EEG). Standard sparsity regularization does not necessarily produce adequate results…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
A celebrated inequality by Payne relates the first eigenvalue of the Dirichlet Laplacian to the first eigenvalue of the buckling problem. Motivated by the goal of establishing a quantitative version of this inequality, we show that Payne's…
In high energy resolution X-ray spectroscopy beamlines of synchrotron radiation facilities, it is important to keep X-ray spectrometer operating in optimal conditions. The adjusting process is normally very time consuming due to the…
Phase aberration is one of the primary sources of image quality degradation in ultrasound, which is induced by spatial variations in sound speed across the heterogeneous medium. This effect disrupts transmitted waves and prevents coherent…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
The ultraspherical spectral method features high accuracy and fast solution. In this article, we determine the sources of error arising from the ultraspherical spectral method and derive its effective condition number, which explains why…
The current paper is the second part of a series of two papers dedicated to 2D problem of diffraction of acoustic waves by a segment bearing impedance boundary conditions. In the first part some preliminary steps were made, namely, the…
For a second-order symmetric strongly elliptic operator A on a smooth bounded open set \Omega in R^n with boundary \Sigma, the mixed problem is defined by a Neumann-type condition on a part Sigma_+ of the boundary and a Dirichlet condition…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
In this paper we show that we can use a modified version of the h-p spectral element method proposed in \cite{duttora1,duttom,duttora2,tomarth} to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal…