Related papers: Graph partitioning using matrix values for precond…
Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…
Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. While there exist well-established spectral algorithms for this problem that give good results, they have traditionally not been well…
The dynamic scaling of distributed computations plays an important role in the utilization of elastic computational resources, such as the cloud. It enables the provisioning and de-provisioning of resources to match dynamic resource…
The efficient solution of moderately large-scale linear systems arising from the KKT conditions in optimal control problems (OCPs) is a critical challenge in robotics. With the stagnation of Moore's law, there is growing interest in…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
In this work, we propose and study a preconditioned framework with a graphic Ginzburg-Landau functional for image segmentation and data clustering by parallel computing. Solving nonlocal models is usually challenging due to the huge…
We describe an approach to parallel graph partitioning that scales to hundreds of processors and produces a high solution quality. For example, for many instances from Walshaw's benchmark collection we improve the best known partitioning.…
Fractional spectral collocation (FSC) method based on fractional Lagrange interpolation has recently been proposed to solve fractional differential equations. Numerical experiments show that the linear systems in FSC become extremely…
We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix $A$ and a possibly dense, rank deficient matrix of the form $\gamma UU^T$, where $\gamma > 0$…
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem.…
Hyperspectral unmixing aims at decomposing a given signal into its spectral signatures and its associated fractional abundances. To improve the accuracy of this decomposition, algorithms have included different assumptions depending on the…
We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…
Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices…
For random graphs distributed according to a stochastic block model, we consider the inferential task of partioning vertices into blocks using spectral techniques. Spectral partioning using the normalized Laplacian and the adjacency matrix…