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In this paper, we study a $\tau$-matrix approximation based preconditioner for the linear systems arising from discretization of unsteady state Riesz space fractional diffusion equation with non-separable variable coefficients. The…

Numerical Analysis · Mathematics 2024-04-18 Xue-Lei Lin , Michael K. Ng

We propose a randomized first order optimization algorithm Gradient Projection Iterative Sketch (GPIS) and an accelerated variant for efficiently solving large scale constrained Least Squares (LS). We provide theoretical convergence…

Optimization and Control · Mathematics 2017-07-18 Junqi Tang , Mohammad Golbabaee , Mike Davies

This paper presents a couple of preconditioning techniques that can be used to enhance the performance of iterative regularization methods applied to image deblurring problems with a variety of point spread functions (PSFs) and boundary…

Numerical Analysis · Mathematics 2022-12-13 Marco Donatelli , Paola Ferrari , Silvia Gazzola

With the commercial availability of mixed precision hardware, mixed precision GMRES-based iterative refinement schemes have emerged as popular approaches for solving sparse linear systems. Existing analyses of these approaches, however, are…

Numerical Analysis · Mathematics 2022-09-02 Erin Carson , Noaman Khan

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…

Numerical Analysis · Mathematics 2025-10-17 Paolo Foschi

Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

Data Structures and Algorithms · Computer Science 2020-03-19 Agniva Chowdhury , Palma London , Haim Avron , Petros Drineas

This paper considers the multi-agent distributed linear least-squares problem. The system comprises multiple agents, each agent with a locally observed set of data points, and a common server with whom the agents can interact. The agents'…

Optimization and Control · Mathematics 2020-12-01 Kushal Chakrabarti , Nirupam Gupta , Nikhil Chopra

Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems. We propose two novel strategies for…

Numerical Analysis · Mathematics 2014-07-31 Bedřich Sousedík , Roger G. Ghanem

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

Machine Learning · Computer Science 2024-07-17 Roberto Esposito , Mattia Cerrato , Marco Locatelli

The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part…

Numerical Analysis · Computer Science 2017-01-09 E. G. Abramov

A fluid-structure interaction (FSI) problem is solved via a monolithic coupling of the fluid, structure, and geometry subproblems. The iterative GMRES solver is accelerated with the FaCSI block preconditioner. In the FaCSI factorization,…

Numerical Analysis · Mathematics 2025-12-02 Axel Klawonn , Jascha Knepper , Lea Saßmannshausen

We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…

Numerical Analysis · Mathematics 2017-08-08 Robert O'Connor

Brown and Walker (1997) showed that GMRES determines a least squares solution of $ A x = b $ where $ A \in {\bf R}^{n \times n} $ without breakdown for arbitrary $ b, x_0 \in {\bf R}^n $ if and only if $A$ is range-symmetric, i.e. $ {\cal…

Numerical Analysis · Mathematics 2024-07-08 Kota Sugihara , Ken Hayami

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…

Numerical Analysis · Mathematics 2017-05-31 Melina Freitag , Patrick Kürschner , Jennifer Pestana

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…

Numerical Analysis · Mathematics 2015-08-11 Bruno Carpentieri , Jia Liao , Masha Sosonkina , Aldo Bonfiglioli

We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated,…

Numerical Analysis · Mathematics 2015-09-01 Paolo Gatto , Jan S. Hesthaven

Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…

Numerical Analysis · Mathematics 2013-11-19 Eugene Vecharynski , Yousef Saad , Masha Sosonkina

We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…

Optimization and Control · Mathematics 2023-01-31 Nikita Doikov , Anton Rodomanov

We propose a time stepping scheme for the space-time systems obtained from Galerkin time-domain boundary element methods for the wave equation. Based on extrapolation, the method proves stable, becomes exact for increasing degrees of…

Numerical Analysis · Mathematics 2020-03-06 Heiko Gimperlein , David Stark

We consider parameterized variational inverse problems that are constrained by partial differential equations (PDEs). We seek to efficiently compute the solution of the inverse problem when auxiliary model parameters, which appear in the…

Numerical Analysis · Mathematics 2026-01-29 Joseph Hart , Alen Alexanderian , Bart van Bloemen Waanders