Related papers: Pipelined, Flexible Krylov Subspace Methods
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…
Structured Cartesian grids are a fundamental component in numerical simulations. Although these grids facilitate straightforward discretization schemes, their na\"{i}ve use in sparse domains leads to excessive memory overhead and…
Hyperparameter tuning of multi-stage pipelines introduces a significant computational burden. Motivated by the observation that work can be reused across pipelines if the intermediate computations are the same, we propose a pipeline-aware…
We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We…
In this paper, we present an advanced high-order compact gas-kinetic scheme (CGKS) for 3D unstructured mixed-element meshes, augmented with a geometric multigrid technique to accelerate steady-state convergence. The scheme evolves…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
We evaluate the performance of the Krylov subspace method by using highly efficient multiple precision sparse matrix-vector multiplication (SpMV). BNCpack is our multiple precision numerical computation library based on MPFR/GMP, which is…
An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…
Generalized linear mixed models (GLMMs) are a widely used tool in statistical analysis. The main bottleneck of many computational approaches lies in the inversion of the high dimensional precision matrices associated with the random…
This paper has proposed the GMRES that augments Krylov subspaces with a set of approximate right singular vectors. The proposed method suppresses the error norms of a linear system of equations. Numerical experiments comparing the proposed…
This survey concerns subspace recycling methods, a popular class of iterative methods that enable effective reuse of subspace information in order to speed up convergence and find good initial guesses over a sequence of linear systems with…
A key consideration in the development of numerical schemes for time-dependent partial differential equations (PDEs) is the ability to preserve certain properties of the continuum solution, such as associated conservation laws or other…
One of the limitations of recycled GCRO methods is the large amount of computation required to orthogonalize the basis vectors of the newly generated Krylov subspace for the approximate solution when combined with those of the recycle…
Krylov subspace methods are considered a standard tool to solve large systems of linear algebraic equations in many scientific disciplines such as image restoration or solving partial differential equations in mechanics of continuum. In the…
A multigrid scheme is proposed for the pressure equation of the incompressible unsteady fluid flow equations, allowing efficient implementation on clusters of modern CPUs, many integrated core devices (MICs), and graphics processing units…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and divergence-free. When…
Gauss-Seidel (GS) relaxation is often employed as a preconditioner for a Krylov solver or as a smoother for Algebraic Multigrid (AMG). However, the requisite sparse triangular solve is difficult to parallelize on many-core architectures…
Model-based reconstruction plays a key role in compressed sensing (CS) MRI, as it incorporates effective image regularizers to improve the quality of reconstruction. The Plug-and-Play and Regularization-by-Denoising frameworks leverage…
Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…