Preconditioners for Krylov subspace methods: An overview

JW Pearson, J Pestana - GAMM‐Mitteilungen, 2020‏ - Wiley Online Library
When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

Analysis of the truncated conjugate gradient method for linear matrix equations

V Simoncini, Y Hao - SIAM Journal on Matrix Analysis and Applications, 2023‏ - SIAM
The matrix-oriented version of the conjugate gradient (CG) method can be used to
approximate the solution to certain linear matrix equations. To limit memory consumption …

Matrix equation techniques for certain evolutionary partial differential equations

D Palitta - Journal of Scientific Computing, 2021‏ - Springer
We show that the discrete operator stemming from time-space discretization of evolutionary
partial differential equations can be represented in terms of a single Sylvester matrix …

A tensor multigrid method for solving Sylvester tensor equations

Y Chen, C Li - IEEE Transactions on Automation Science and …, 2023‏ - ieeexplore.ieee.org
In this paper, we propose a tensor multigrid method and an iterative tensor multigrid method
to solve the Sylvester tensor equations which may arise from the discretization of high order …

Compress‐and‐restart block Krylov subspace methods for Sylvester matrix equations

D Kressner, K Lund, S Massei… - Numerical Linear Algebra …, 2021‏ - Wiley Online Library
Summary Block Krylov subspace methods (KSMs) comprise building blocks in many state‐of‐
the‐art solvers for large‐scale matrix equations as they arise, for example, from the …

Risk-Adaptive Experimental Design for High-Consequence Systems: LDRD Final Report

DP Kouri, JD Jakeman, JG Huerta, CB Smith, TF Walsh… - 2021‏ - osti.gov
Constructing accurate statistical models of critical system responses typically requires an
enormous amount of data from physical experiments or numerical simulations …

[PDF][PDF] Schwarz methods, Schur complements, preconditioning and numerical linear algebra

M Outrata - 2022‏ - archive-ouverte.unige.ch
This thesis can be divided into two parts:(optimized) Schwarz methods and related topics
and preconditioning of the stage equations of implicit Runge-Kutta methods. Schwarz …

Spectral analysis of implicit 2 stage block Runge-Kutta preconditioners

MJ Gander, M Outrata - Linear Algebra and its Applications, 2024‏ - Elsevier
We analyze the recently introduced family of preconditioners in [15] for the stage equations
of implicit Runge-Kutta methods for two stage methods. We give explicit formulas for the …

Sylvester-Preconditioned Adaptive-Rank Implicit Time Integrators for Advection-Diffusion Equations with Inhomogeneous Coefficients

HE Kahza, JM Qiu, L Chacon, W Taitano - arxiv preprint arxiv:2410.19662, 2024‏ - arxiv.org
We consider the adaptive-rank integration of general time-dependent advection-diffusion
partial differential equations (PDEs) with spatially variable coefficients. We employ a …

A subspace-conjugate gradient method for linear matrix equations

D Palitta, M Iannacito, V Simoncini - arxiv preprint arxiv:2501.02938, 2025‏ - arxiv.org
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in
numerical linear algebra, and it is a largely open problem. We propose a new iterative …