Related papers: Sampling patterns for Zernike-like bases in non-st…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain…
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a plurisubharmonic weight. In particular, these spaces do not…
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First, we introduce a validated Matrix Multiplication Transform…
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of…
We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
Due to the massive increase in astronomical images (such as James Webb and Solar Dynamic Observatory), automatic image description is essential for solar and astronomical. Zernike moments (ZMs) are unique due to the orthogonality and…
In this paper we develop a plane wave type method for discretization of homogeneous Helmholtz equations with variable wave numbers. In the proposed method, local basis functions (on each element) are constructed by the geometric optics…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
Sample patterns have many uses in Computer Graphics, ranging from procedural object placement over Monte Carlo image synthesis to non-photorealistic depiction. Their properties such as discrepancy, spectra, anisotropy, or progressiveness…
The major sources causing deterioration of optical quality in extremely large optical telescopes are misadjustments of the mirrors, deformations of monolithic mirrors, and misalignments of segments in segmented mirrors. For active optics…
This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density…
The need for fast, effective and accurate surveys have become increasingly necessary. A major part of the research is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
In this paper, we develop a theoretical analysis to efficiently handle superpositions of waves with concentrated wavevector and frequency spectra, allowing an easy analytical description of fields with interesting transverse profiles.…