Related papers: Preconditioned Linear Solves for Parametric Model …
Numerous practical medical problems often involve data that possess a combination of both sparse and non-sparse structures. Traditional penalized regularizations techniques, primarily designed for promoting sparsity, are inadequate to…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…
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…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
In ill-posed dynamic inverse problems expected spatial features and temporal correlation between frames can be leveraged to improve the quality of the computed solution, in particular when the available data are limited and the…
The discontinuous Galerkin time-stepping method has many advantageous properties for solving parabolic equations. However, it requires the solution of a large nonsymmetric system at each time-step. This work develops a fully robust and…
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual…
We propose a new method for preconditioning Kaczmarz method by sketching. Kaczmarz method is a stochastic method for solving overdetermined linear systems based on a sampling of matrix rows. The standard approach to speed up convergence of…
We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…
This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures,…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
It was recently established that for convex optimization problems with sparse optimal solutions (be it entry-wise sparsity or matrix rank-wise sparsity) it is possible to design first-order methods with linear convergence rates that depend…
The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li,~Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…
A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…
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…
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…