Related papers: An efficient parallel algorithm for computing dete…
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We…
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…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
Prony's method is a standard tool exploited for solving many imaging and data analysis problems that result in parameter identification in sparse exponential sums $$f(k)=\sum_{j=1}^{T}c_{j}e^{-2\pi i\langle t_{j},k\rangle},\quad k\in…
In this paper, we consider an approach to the parallelizing of the algorithms realizing the modified probability changigng method with adaptation and partial rollback procedure for constrained pseudo-Boolean optimization problems. Existing…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…
We give a quantum-inspired $O(n^4)$ algorithm computing the Tutte polynomial of a lattice path matroid, where $n$ is the size of the ground set of the matroid. Furthermore, this can be improved to $O(n^2)$ arithmetic operations if we…
Many emerging computer applications require the processing of large numbers, larger than what a CPU can handle. In fact, the top of the line PCs can only manipulate numbers not longer than 32 bits or 64 bits. This is due to the size of the…
We revisit the problem of finding optimal strategies for deterministic Markov Decision Processes (DMDPs), and a closely related problem of testing feasibility of systems of $m$ linear inequalities on $n$ real variables with at most two…
Computational protein structure determination involves optimization in a problem space much too large to exhaustively search. Existing approaches include optimization algorithms such as gradient descent and simulated annealing, but these…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…