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We construct a locally-lexicographic SSOR preconditioner to accelerate the parallel iterative solution of linear systems of equations for two improved discretizations of lattice fermions: the Sheikholeslami-Wohlert scheme where a…

High Energy Physics - Lattice · Physics 2009-10-31 W. Bietenholz , N. Eicker , A. Frommer , Th. Lippert , B. Medeke , K. Schilling , G. Weuffen

The Lippmann-Schwinger equation is an integral equation formulation for acoustic and electromagnetic scattering from an inhomogeneous media and quantum scattering from a localized potential. We present the sparsifying preconditioner for…

Numerical Analysis · Mathematics 2014-09-17 Lexing Ying

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

Optimization and Control · Mathematics 2026-03-20 Jian Chen , Xinmin Yang

We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…

Numerical Analysis · Mathematics 2018-05-08 Daria A. Sushnikova , Ivan V. Oseledets

We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is based on an augmented Lagrangian approach of the full…

Numerical Analysis · Mathematics 2025-12-03 Alexander D. Lindsay , Sander Rhebergen , Ben S. Southworth

An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time…

Numerical Analysis · Mathematics 2025-07-31 Weizhang Huang , Zhuoran Wang

This paper deals with the fast solution of linear systems associated with the mass matrix, in the context of isogeometric analysis. We propose a preconditioner that is both efficient and easy to implement, based on a diagonal-scaled…

Numerical Analysis · Mathematics 2020-11-30 Gabriele Loli , Giancarlo Sangalli , Mattia Tani

We examine a special case of the multilevel factor model, with covariance given by multilevel low rank (MLR) matrix~\cite{parshakova2023factor}. We develop a novel, fast implementation of the expectation-maximization algorithm, tailored for…

Machine Learning · Statistics 2025-08-26 Tetiana Parshakova , Trevor Hastie , Stephen Boyd

Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices…

Numerical Analysis · Mathematics 2025-10-17 Hayden Henson , Ronald B. Morgan

We consider the problem of finding the optimal diagonal preconditioner for a positive definite matrix. Although this problem has been shown to be solvable and various methods have been proposed, none of the existing approaches are scalable…

Numerical Analysis · Mathematics 2024-11-07 Wenzhi Gao , Zhaonan Qu , Madeleine Udell , Yinyu Ye

In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…

Numerical Analysis · Mathematics 2013-12-06 Luca Bergamaschi , Angeles Martinez

Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…

Numerical Analysis · Mathematics 2025-05-28 Marc A. Tunnell , David F. Gleich

The convergence rates of iterative methods for solving a linear system $\mathbf{A} x = b$ typically depend on the condition number of the matrix $\mathbf{A}$. Preconditioning is a common way of speeding up these methods by reducing that…

Optimization and Control · Mathematics 2021-11-04 Arun Jambulapati , Jerry Li , Christopher Musco , Aaron Sidford , Kevin Tian

This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann-Schwinger equation, this paper generalizes that…

Numerical Analysis · Mathematics 2018-11-14 Fei Liu , Lexing Ying

We study the solution of large symmetric positive-definite linear systems in a matrix-free setting with a limited iteration budget. We focus on the preconditioned conjugate gradient (PCG) method with spectral preconditioning. Spectral…

Numerical Analysis · Mathematics 2026-04-01 Youssef Diouane , Selime Gürol , Oussama Mouhtal , Dominique Orban

In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…

Numerical Analysis · Mathematics 2018-10-16 Erik Eikeland , Leszek Marcinkowski , Talal Rahman

In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het- erogeneous media. Our approach uses the technique of…

Numerical Analysis · Mathematics 2016-01-14 Johannes Kraus , Raytcho Lazarov , Maria Lymbery , Svetozar Margenov , Ludmil Zikatanov

In this paper, we propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify a sparse control architecture that optimizes the closed-loop performance while…

Optimization and Control · Mathematics 2022-08-22 Yi Guo , Ognjen Stanojev , Gabriela Hug , Tyler Summers

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible…

Numerical Analysis · Mathematics 2020-07-28 Matteo Frigo , Nicola Castelletto , Massimiliano Ferronato , Joshua A. White

While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…

Numerical Analysis · Mathematics 2024-01-15 Andreas Frommer , Gustavo Ramirez-Hidalgo , Marcel Schweitzer , Manuel Tsolakis