Related papers: An algorithm for evaluating Gram matrices in Verma…
Performing analog computations with metastructures is an emerging wave-based paradigm for solving mathematical problems. For such devices, one major challenge is their reconfigurability, especially without the need for a priori mathematical…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the…
We study distributed training of deep learning models in time-constrained environments. We propose a new algorithm that periodically pulls workers towards the center variable computed as a weighted average of workers, where the weights are…
In this paper, we compute the Gram determinants associated to each cell module of the Birman-Wenzl algebras. As a by-product, we give the necessary and sufficient condition for semisimple Birman-Wenzl algebras over an arbitrary field.
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
To appear in Theory and Practice of Logic Programming (TPLP). Several Prolog interpreters are based on the Warren Abstract Machine (WAM), an elegant model to compile Prolog programs. In order to improve the performance several strategies…
Let K be a subfield of the complex numbers, and let D be the Weyl algebra of K-linear differential operators on K[x_1,...,x_n]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite…
The FLAME methodology makes it possible to derive provably correct algorithms from a formal description of a linear algebra problem. So far, the methodology has been successfully used to automate the derivation of direct algorithms such as…
Inspired by the latest developments in multilevel Monte Carlo (MLMC) methods and randomised sketching for linear algebra problems we propose a MLMC estimator for real-time processing of matrix structured random data. Our algorithm is…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
Using explicit expressions for a class of singular vectors of the $N=2$ (untwisted) algebra and following the approach of Malikov-Feigin-Fuchs and Kent, we show that the analytically extended Verma modules contain two linearly independent…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebra $G_{2(2)}$ which is split real form of $G_2$. We give the classification of reducible…
Ihe first author presented an efficient algorithm for computing involutive (and reduced Groebner) bases. In this paper, we consider a modification of this algorithm which simplifies matters to understand it and to implement. We prove…
This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…
In this paper we develop an accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for solving quadratic programs called superADMM. Unlike standard ADMM QP solvers, superADMM uses a novel dynamic weighting method that…
This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on…