Related papers: A new framework for the computation of Hessians

Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

The availability of larger and larger graph datasets, growing exponentially over the years, has created several new algorithmic challenges to be addressed. Sequential approaches have become unfeasible, while interest on parallel and…

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…

Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebro-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra, and the latter was…

Dataflow-oriented spatial architectures are the emerging paradigm for higher computation performance and efficiency. AMD Versal AI Engine is a commercial spatial architecture consisting of tiles of VLIW processors supporting SIMD operations…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

This paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…

In this paper we present a new dynamical systems algorithm for clustering in hyperspectral images. The main idea of the algorithm is that data points are \`pushed\' in the direction of increasing density and groups of pixels that end up in…

The synthesis of optimization algorithms typically follows a design-first-analyze-later approach, which often obscures fundamental performance limitations and hinders the systematic design of algorithms operating at the achievable…

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…

Clustering is a fundamental task in network analysis, essential for uncovering hidden structures within complex systems. Edge clustering, which focuses on relationships between nodes rather than the nodes themselves, has gained increased…

This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three…

A randomized algorithm for computing a data sparse representation of a given rank structured matrix $A$ (a.k.a. an $H$-matrix) is presented. The algorithm draws on the randomized singular value decomposition (RSVD), and operates under the…

This paper presents a novel optimization for differentiable programming named coarsening optimization. It offers a systematic way to synergize symbolic differentiation and algorithmic differentiation (AD). Through it, the granularity of the…

A variety of dimensionality reduction techniques have been applied for computations involving large matrices. The underlying matrix is randomly compressed into a smaller one, while approximately retaining many of its original properties. As…

This paper shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new…

Embedding tables are used by machine learning systems to work with categorical features. In modern Recommendation Systems, these tables can be very large, necessitating the development of new methods for fitting them in memory, even during…

A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…

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…