相关论文: Function integration, reconstruction and approxima…

We study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to…

We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…

This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…

Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in particular the Gibbs phenomenon, is being intensively…

The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a…

Building on recent advances in reduced density matrix theory, we develop a geometric framework for describing strongly correlated lattice bosons. We first establish that translational symmetry, together with a fixed pair interaction,…

We introduce compositional tensor trains (CTTs) for the approximation of multivariate functions, a class of models obtained by composing low-rank functions in the tensor-train format. This format can encode standard approximation tools,…

We introduce and analyze a mesh-free two-level hybrid Chebyshev-Tucker tensor representation for approximating multivariate functions, which combines tensor-product Chebyshev interpolation with the low-rank Tucker decomposition of the…

Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over \mathbb{R}^{N}…

This work proposes the extended functional tensor train (EFTT) format for compressing and working with multivariate functions on tensor product domains. Our compression algorithm combines tensorized Chebyshev interpolation with a low-rank…

We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…

We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…

For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional…

It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the…

We propose a very simple randomised data structure that stores an approximation from above of a lattice-valued function. Computing the function value requires a constant number of steps, and the error probability can be balanced with space…

Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…

Transformers are widely used across data modalities, and yet the principles distilled from text models often transfer imperfectly to models trained to other modalities. In this paper, we analyze Transformers through the lens of rank…

Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs…

This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…

Dense retrieval compresses texts into single embeddings ranked by cosine similarity. While efficient for recall, this interface is brittle for identity-level matching: minimal compositional edits (negation, role swaps) flip meaning yet…