Related papers: Remarkable upper bounds for the interpolation erro…
Software model checking is a challenging problem, and generating relevant invariants is a key factor in proving the safety properties of a program. Program invariants can be obtained by various approaches, including lightweight procedures…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
We present a new analysis of the stability of extended Floater-Hormann interpolants, in which both noisy data and rounding errors are considered. Contrary to what is claimed in the current literature, we show that the Lebesgue constant of…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
We approximate the uniform measure on an equilateral triangle by a measure supported on $n$ points. We find the optimal sets of points ($n$-means) and corresponding approximation (quantization) error for $n\leq4$, give numerical…
There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
This paper presents an extension of a recently developed high order finite difference method for the wave equation on a grid with non-conforming interfaces. The stability proof of the existing methods relies on the interpolation operators…
An explicit upper bound is derived for the modulus of divided difference for a smooth(not necessarily analytic) function defined on a smooth Jordan arc (or a smooth Jordan curve) in the complex plane. As an immediate application, an error…
We establish improved convergence rates for curved boundary element methods applied to the three-dimensional (3D) Laplace and Helmholtz equations with smooth geometry and data. Our analysis relies on a precise analysis of the consistency…
We consider a cross interpolation of high-dimensional arrays in the tensor train format. We prove that the maximum-volume choice of the interpolation sets provides the quasioptimal interpolation accuracy, that differs from the best possible…
Video frame interpolation, the task of synthesizing new frames in between two or more given ones, is becoming an increasingly popular research target. However, the current evaluation of frame interpolation techniques is not ideal. Due to…
The aim of this paper is a construction of quartic parametric polynomial interpolants of a circular arc, where two boundary points of a circular arc are interpolated. For every unit circular arc of inner angle not greater than $\pi$ we find…
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…
One classical measure of the quality of an interpolating function is its Lipschitz constant. In this paper we consider interpolants with additional smoothness requirements, in particular that their derivatives be Lipschitz. We show that…
We prove stability estimates for the ENO reconstruction and ENO interpolation procedures. In particular, we show that the jump of the reconstructed ENO pointvalues at each cell interface has the same sign as the jump of the underlying cell…
In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly…