Related papers: Interpolation-Based GR(1) Assumptions Refinement
Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…
This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…
In coherent diffractive imaging (CDI) the resolution of the reconstructed object is limited by the numerical aperture of the experimental setup. We present here a theoretical and numerical study for achieving super-resolution by…
This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…
Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt…
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data…
A retrieval model should not only interpolate the training data but also extrapolate well to the queries that are different from the training data. While neural retrieval models have demonstrated impressive performance on ad-hoc search…
This article presents novel proof methods for estimating interpolation errors, predicated on the understanding that one has already studied foundational error analysis using the finite element method.
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of…
A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Pade and other interpolation schemes. A unified view of these various…
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…
We show that the vast majority of extensions of the description logic $\mathcal{EL}$ do not enjoy the Craig interpolation nor the projective Beth definability property. This is the case, for example, for $\mathcal{EL}$ with nominals,…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…