Related papers: Parallel algorithms for normalization
This paper presents algorithms for temporal parallelization of Bayesian smoothers. We define the elements and the operators to pose these problems as the solutions to all-prefix-sums operations for which efficient parallel scan-algorithms…
Globally normalized neural sequence models are considered superior to their locally normalized equivalents because they may ameliorate the effects of label bias. However, when considering high-capacity neural parametrizations that condition…
We present a novel local improvement scheme for the perfectly balanced graph partitioning problem. This scheme encodes local searches that are not restricted to a balance constraint into a model allowing us to find combinations of these…
Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of…
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…
We present an effective algorithm for computing the standard cohomology spaces of finitely generated Lie (super) algebras over a commutative field K of characteristic zero. In order to reach explicit representatives of some generators of…
We provide new insight into a {\em generalized conditional subgradient} algorithm and a {\em generalized mirror descent} algorithm for the convex minimization problem \[ \min_x \; \{f(Ax) + h(x)\}.\] As Bach showed in [{\em SIAM J. Optim.},…
Many real-world optimization models contain exploitable sparsity and block structure, but this structure is often obscured in algebraic form, limiting the effectiveness of modern parallel algorithms. We propose an automatic pipeline that…
We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials…
We present parallel and sequential dense QR factorization algorithms for tall and skinny matrices and general rectangular matrices that both minimize communication, and are as stable as Householder QR. The sequential and parallel algorithms…
Many practical applications require solving an optimization over large and high-dimensional data sets, which makes these problems hard to solve and prohibitively time consuming. In this paper, we propose a parallel distributed algorithm…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
We generalize Grover's unstructured quantum search algorithm to enable it to use an arbitrary starting superposition and an arbitrary unitary matrix simultaneously. We derive an exact formula for the probability of the generalized Grover's…
Sparse, irregular graphs show up in various applications like linear algebra, machine learning, engineering simulations, robotic control, etc. These graphs have a high degree of parallelism, but their execution on parallel threads of modern…
We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…
The problem of Bayesian filtering and smoothing in nonlinear models with additive noise is an active area of research. Classical Taylor series as well as more recent sigma-point based methods are two well-known strategies to deal with these…
We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…
Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…
Although it is relatively easy to apply, the gradient method often displays a disappointingly slow rate of convergence. Its convergence is specially based on the structure of the matrix of the algebraic linear system, and on the choice 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…