Related papers: GPMR: An Iterative Method for Unsymmetric Partitio…

In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian…

In this paper, to solve a broad class of complex symmetric linear systems, we recast the complex system in a real formulation and apply the generalized successive overrelaxation (GSOR) iterative method to the equivalent real system. We then…

We propose a simple doubly stochastic block Gauss--Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber…

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

We present an algorithm for recovering planted solutions in two well-known models, the stochastic block model and planted constraint satisfaction problems, via a common generalization in terms of random bipartite graphs. Our algorithm…

Recovering a low rank matrix from a subset of its entries, some of which may be corrupted, is known as the robust matrix completion (RMC) problem. Existing RMC methods have several limitations: they require a relatively large number of…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

We present a recursive way to partition hypergraphs which creates and exploits hypergraph geometry and is suitable for many-core parallel architectures. Such partitionings are then used to bring sparse matrices in a recursive Bordered Block…

The Nonlinear GMRES (NGMRES) proposed by Washio and Oosterlee [Electron. Trans. Numer. Anal, 6(271-290), 1997] is an acceleration method for fixed point iterations. It has been demonstrated to be effective, but its convergence properties…

It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible $H-$matrices…

Multi-block separable convex problems recently received considerable attention. This class of optimization problems minimizes a separable convex objective function with linear constraints. The algorithmic challenges come from the fact that…

Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data…

In this paper, we propose RFF-GP-HSMM, a fast unsupervised time-series segmentation method that incorporates random Fourier features (RFF) to address the high computational cost of the Gaussian process hidden semi-Markov model (GP-HSMM).…

In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…

Block matrix structure is commonly arising is various physics and engineering applications. There are various advantages in preserving the blocks structure while computing the inversion of such partitioned matrices. In this context, using…

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…