相关论文: Piecewise Polynomial Interpolation Function Approa…

In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…

We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal…

Deep neural networks are increasingly used in safety-critical domains such as robotics and scientific modeling, where strict adherence to output constraints is essential. Methods like POLICE, which are tailored for single convex regions,…

We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…

We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…

We consider the problem of obtaining interpolation constraints for function classes, i.e., necessary and sufficient constraints that a set of points, function values and (sub)gradients must satisfy to ensure the existence of a global…

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…

Selective inference (SI) has been actively studied as a promising framework for statistical hypothesis testing for data-driven hypotheses. The basic idea of SI is to make inferences conditional on an event that a hypothesis is selected. In…

Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named \emph{extrapolated proportional-integral projected gradient method…

We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…

The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…

Operating envelope is an important concept in industrial operations. Accurate identification for operating envelope can be extremely beneficial to stakeholders as it provides a set of operational parameters that optimizes some key…

The polarization decomposition of arbitrary binary-input memoryless channels (BMCs) is studied in this work. By introducing the polarization factor (PF), defined in terms of the conditional entropy of the channel output under various input…

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the…

We introduce an iterative method to solve problems in small-strain non-linear elasticity, termed ``Phase-Space Iterations'' (PSIs). The method is inspired by recent work in data-driven computational mechanics, which reformulated the classic…

In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…

Aligning protein-protein interaction (PPI) networks of different species has drawn a considerable interest recently. This problem is important to investigate evolutionary conserved pathways or protein complexes across species, and to help…