Related papers: Recent Advances in Debordering Methods
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a…
The analysis of the decoding failure rate of the bit-flipping algorithm has received increasing attention. For a binary linear code we consider the minimum number of rows in a parity-check matrix such that the bit-flipping algorithm is able…
We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. First, we propose novel bounding algorithms based on Lagrangian Decomposition. Previous works have used…
Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit…
The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…
Blind motion deblurring is one of the most basic and challenging problems in image processing and computer vision. It aims to recover a sharp image from its blurred version knowing nothing about the blur process. Many existing methods use…
Joint space trajectory optimization under end-effector task constraints leads to a challenging non-convex problem. Thus, a real-time adaptation of prior computed trajectories to perturbation in task constraints often becomes intractable.…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…
Tensors decompositions are a class of tools for analysing datasets of high dimensionality and variety in a natural manner, with the Canonical Polyadic Decomposition (CPD) being a main pillar. While the notion of CPD is closely intertwined…
In La G\'eom\'etrie, Descartes proposed a balance between geometric constructions and symbolic manipulation with the introduction of suitable ideal machines. In modern terms, that is a balance between analog and symbolic computation.…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
Reducing communication - either between levels of a memory hierarchy or between processors over a network - is a key component of performance optimization (in both time and energy) for many problems, including dense linear algebra, particle…
This is an overview of recent developments regarding the complexity of matrix multiplication, with an emphasis on the uses of algebraic geometry and representation theory in complexity theory.
Border basis schemes are open subschemes of the Hilbert scheme of $\mu$ points in an affine space $\mathbb{A}^n$. They have easily describable systems of generators of their vanishing ideals for a natural embedding into a large affine space…
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The…
In the general submatrix detection problem, the task is to detect the presence of a small $k \times k$ submatrix with entries sampled from a distribution $\mathcal{P}$ in an $n \times n$ matrix of samples from $\mathcal{Q}$. This…