Related papers: Optimized Multivariate Polynomial Determinant on G…
Given a square, nonsingular matrix of univariate polynomials $\mathbf{F}\in\mathbb{K}[x]^{n\times n}$ over a field $\mathbb{K}$, we give a deterministic algorithm for finding the determinant of $\mathbf{F}$. The complexity of the algorithm…
We propose a first-order method for convex optimization, where instead of being restricted to the gradient from a single parameter, gradients from multiple parameters can be used during each step of gradient descent. This setup is…
We survey and unify recent results on the existence of accurate algorithms for evaluating multivariate polynomials, and more generally for accurate numerical linear algebra with structured matrices. By "accurate" we mean that the computed…
In this paper, we show the effectiveness of a pipeline implementation of Dynamic Programming (DP) on GPU. As an example, we explain how to solve a matrix-chain multiplication (MCM) problem by DP on GPU. This problem can be sequentially…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
The focus of my PhD thesis is on exploring parallel approaches to efficiently solve problems modeled by constraints and presenting a new proposal. Current solvers are very advanced; they are carefully designed to effectively manage the…
This paper is devoted to computational algorithms designed to describe the classical Ising magnet in some specific cases when an additional macroscopic restriction in form of constant charge density exists in the system. We developed and…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
Computational Pangenomics is an emerging field that studies genetic variation using a graph structure encompassing multiple genomes. Visualizing pangenome graphs is vital for understanding genome diversity. Yet, handling large graphs can be…
Supporting multiple partial computations efficiently at each of the workers is a keystone in distributed coded computing in order to speed up computations and to fully exploit the resources of heterogeneous workers in terms of…
Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…
The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the…
Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally…
B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these…
We develop a novel parallel resampling algorithm for fully parallelized particle filters, which is designed with GPUs (graphics processing units) or similar parallel computing devices in mind. With our new algorithm, a full cycle of…
Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash},…