Related papers: Error Control of Iterative Linear Solvers for Inte…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…
The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…
We present two minimum residual methods for solving sequences of shifted linear systems, the right-preconditioned shifted GMRES and shifted recycled GMRES algorithms which use a seed projection strategy often employed to solve multiple…
We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner…
In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a discontinuous Galerkin finite element approximation in…
This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the…
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…
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…
In this paper, we develop a (preconditioned) GMRES solver based on integer arithmetic, and introduce an iterative refinement framework for the solver. We describe the data format for the coefficient matrix and vectors for the solver that is…
The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…
The convergence of GMRES for solving linear systems can be influenced heavily by the structure of the right hand side. Within the solution of eigenvalue problems via inverse iteration or subspace iteration, the right hand side is generally…
Support for lower precision computation is becoming more common in accelerator hardware due to lower power usage, reduced data movement and increased computational performance. However, computational science and engineering (CSE) problems…
This study utilized the Gaussian Processes (GPs) regression framework to establish stochastic error bounds between the actual and predicted state evolution of nonlinear systems. These systems are embedded in the linear parameter-varying…
With the emergence of mixed precision capabilities in hardware, iterative refinement schemes for solving linear systems $Ax=b$ have recently been revisited and reanalyzed in the context of three or more precisions. These new analyses show…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…