Related papers: Error bounds for spectral enhancement which are ba…
Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…
We analyse the wavelet shrinkage algorithm of Donoho and Johnstone in order to assess the quality of the reconstruction of a signal obtained from noisy samples. We prove deviation bounds for the maximum of the squares of the error, and for…
This paper is devoted to proving convergence rates of variational and iterative regularization methods under variational source conditions VSCs for inverse problems whose linearization satisfies a range invariance condition. In order to…
Absolute value equations, due to their relation to the linear complementarity problem, have been intensively studied recently. In this paper, we present error bounds for absolute value equations. Along with the error bounds, we introduce an…
In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…
We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
Dimensionality reduction is critical for deploying dense retrieval systems at scale, yet mainstream post-hoc methods face a fundamental trade-off: principal component analysis (PCA) preserves dominant variance but underutilizes…
Using Fisher information and the Cram\'er-Rao lower bound, we analyse fundamental precision limits in the determination of spectral parameters in inelastic optical scattering. General analytic formulae are derived which account for the…
We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any…
Simple bounds are obtained for the integral $\int_0^x\mathrm{e}^{-\gamma t}t^\nu I_\nu(t)\,\mathrm{d}t$, $x>0$, $\nu>-1/2$, $0\leq\gamma<1$, together with a natural generalisation of this integral. In particular, we obtain an upper bound…
A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
We construct $n$-node graphs on which any $O(n)$-size spanner has additive error at least $+\Omega(n^{3/17})$, improving on the previous best lower bound of $\Omega(n^{1/7})$ [Bodwin-Hoppenworth FOCS '22]. Our construction completes the…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
Twenty-one-centimetre signals from the Epoch of Reionization (EoR) are expected to be detected in the low-frequency radio window by the next-generation interferometers, particularly the Square Kilometre Array (SKA). However, precision data…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…
The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.
We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a reduction in the interconnection between the degrees of freedom of the mesh, which…