Related papers: Computational linear algebra over finite fields
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
We propose an efficient dual algorithm for ELP based on Fast Gradient Method. The basic idea - to solve properly regularized dual problem.
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of…
We present an algorithm that decides whether a finitely generated linear group over an infinite field is solvable-by-finite: a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
A simple iteration methodology for the solution of a set of a linear algebraic equations is presented. The explanation of this method is based on a pure geometrical interpretation and pictorial representation. Convergence using this method…
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…
We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing…
We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under…
We consider the scenario in which a set of sources generate messages in a network and a receiver node demands an arbitrary linear function of these messages. We formulate an algebraic test to determine whether an arbitrary network can…
What is computable with limited resources? How can we verify the correctness of computations? How to measure computational power with precision? Despite the immense scientific and engineering progress in computing, we still have only…
We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of $\mathbb{Q}$ that are random according to our definition. We show that there are noncomputable algebraic…
We survey classical and recent developments in numerical linear algebra, focusing on two issues: computational complexity, or arithmetic costs, and numerical stability, or performance under roundoff error. We present a brief account of the…