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Approximate Bayesian computation (ABC) refers to a family of inference methods used in the Bayesian analysis of complex models where evaluation of the likelihood is difficult. Conventional ABC methods often suffer from the curse of…
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…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
We consider the following problem: from a given set of gene families trees on a set of genomes, find a first speciation, that splits these genomes into two subsets, that minimizes the number of gene duplications that happened before this…
An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant…
We introduce a subexponential algorithm for geometric solving of multivariate polynomial equation systems whose bit complexity depends mainly on intrinsic geometric invariants of the solution set. From this algorithm, we derive a new…
We present an efficient algorithm for computing the leading monomials of a minimal Groebner basis of a generic sequence of homogeneous polynomials. Our approach bypasses costly polynomial reductions by exploiting structural properties…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time between consecutive occurrences of the same edge. This NP-hard…
Cardinal's factorization algorithm of 1996 splits a univariate polynomial into two factors with root sets separated by the imaginary axis, which is an important goal itself and a basic step toward root-finding. The novelty of the algorithm…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
In this paper, we explore polynomial accelerators that are well-suited for parallel computations, specifically as smoothers in Algebraic MultiGrid (AMG) preconditioners. These accelerators address a minimax problem, initially formulated in…
We study the non-linear extension of integer programming with greatest common divisor constraints of the form $\gcd(f,g) \sim d$, where $f$ and $g$ are linear polynomials, $d$ is a positive integer, and $\sim$ is a relation among $\leq, =,…
Univariate polynomial root-finding has been studied for four millennia and very intensively in the last decades. Our new near-optimal root-finders approximate all zeros of a polynomial p almost as fast as one accesses its coefficients with…
The Paterson--Stockmeyer method is an evaluation scheme for matrix polynomials with scalar coefficients that arise in many state-of-the-art algorithms based on polynomial or rational approximation, for example, those for computing…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
Suppose $F:=(f_1,\ldots,f_n)$ is a system of random $n$-variate polynomials with $f_i$ having degree $\leq\!d_i$ and the coefficient of $x^{a_1}_1\cdots x^{a_n}_n$ in $f_i$ being an independent complex Gaussian of mean $0$ and variance…