Related papers: Interval Superposition Arithmetic
Interval-valued computing is a relatively new computing paradigm. It uses finitely many interval segments over the unit interval in a computation as data structure. The satisfiability of Quantified Boolean formulae and other hard problems,…
We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of "factoring"…
This work proposes a non-iterative strategy for missing value imputations which is guided by similarity between observations, but instead of explicitly determining distances or nearest neighbors, it assigns observations to overlapping…
Aggregations of flexible loads can provide several power system services through demand response programs, for example load shifting and curtailment. The capabilities of demand response should therefore be represented in system operators'…
We present a new method for embedding a causal set into Minkowski spacetime. The method is similar to a previously presented method, but is simpler and provides better embedding results. The method uses spacetime volumes to define causal…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
This paper develops and compares algorithms to compute inner approximations of the Minkowski sum of convex polytopes. As an application, the paper considers the computation of the feasibility set of aggregations of distributed energy…
We study the following problem. Given a multiset $M$ of non-negative integers, decide whether there exist and, in the positive case, compute two non-trivial multisets whose Minkowski sum is equal to $M$. The Minkowski sum of two multisets A…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
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…
In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains $\Omega \subseteq \RR^N$, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree…
This paper develops a comprehensive probabilistic setup to compute approximating functions in active subspaces. Constantine et al. proposed the active subspace method in (Constantine et al., 2014) to reduce the dimension of computational…
Cost-based image patch matching is at the core of various techniques in computer vision, photogrammetry and remote sensing. When the subpixel disparity between the reference patch in the source and target images is required, either the cost…
Video Frame Interpolation synthesizes non-existent images between adjacent frames, with the aim of providing a smooth and consistent visual experience. Two approaches for solving this challenging task are optical flow based and kernel-based…
We introduce a new class of optimization problems called integer Minkowski programs. The formulation of such problems involves finitely many integer variables and nonlinear constraints involving functionals defined on families of discrete…
We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…
Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…