Related papers: GPMR: An Iterative Method for Unsymmetric Partitio…
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…
We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian…
The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application…
In this work, we propose new variants of Anderson acceleration and nonlinear GMRES for general fixed-point iterations, based on modified least-squares problems associated with the methods. To solve the underlying linear systems, we apply…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…
Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and…
In this paper we study the impact of two types of preconditioning on the numerical solution of large sparse augmented linear systems. The first preconditioning matrix is the lower triangular part whereas the second is the product of the…
In this work, we develop an alternating nonlinear Generalized Minimum Residual (NGMRES) algorithm with depth $m$ and periodicity $p$, denoted by aNGMRES($m, p$), applied to linear systems. We provide a theoretical analysis to quantify by…
Geometric matrix completion (GMC) has been proposed for recommendation by integrating the relationship (link) graphs among users/items into matrix completion (MC). Traditional GMC methods typically adopt graph regularization to impose…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
With a greedy strategy to construct control index set of coordinates firstly and then choosing the corresponding column submatrix in each iteration, we present a greedy block Gauss-Seidel (GBGS) method for solving large linear least squares…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…
Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…