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The choice of relaxation parameter in the projected successive overrelaxation (PSOR) method for nonnegative quadratic programming problems is problem-dependent. We present novel adaptive PSOR algorithms that adaptively control the…

Optimization and Control · Mathematics 2024-09-10 Yuto Miyatake , Tomohiro Sogabe

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

Numerical Analysis · Computer Science 2015-10-06 Nicolas Ray , Sokolov Dmitry

This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…

Numerical Analysis · Mathematics 2021-10-08 Eisa Khosravi Dehdezi , Saeed Karimi

Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and…

Quantum Physics · Physics 2022-06-29 Xiao-Qi Liu , Jing Wang , Ming Li , Shu-Qian Shen , Weiguo Li , Shao-Ming Fei

In this paper generalization of Jacobi and Gauss-Seidel methods, introduced by Salkuyeh in 2007, is studied. In particular, convergence criteria for these methods are discussed. A generalization of successive overrelaxation~(SOR) method is…

Numerical Analysis · Mathematics 2018-06-21 Manideepa Saha , Jahnavi Chakrabarty

We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…

Numerical Analysis · Mathematics 2016-09-23 Man-Chung Yeung , Craig C. Douglas , Long Lee

The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…

Numerical Analysis · Mathematics 2018-09-19 Navneet Pratap Singh , Kapil Ahuja

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…

Numerical Analysis · Mathematics 2022-08-26 Stefanos Nikolopoulos , Ioannis Kalogeris , Vissarion Papadopoulos , George Stavroulakis

Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…

Numerical Analysis · Mathematics 2008-01-28 Nassif Ghoussoub , Amir Moradifam

This study concerns the fast and accurate solution of the line radiation transfer problem, under non-LTE conditions. We propose and evaluate an alternative iterative scheme to the classical ALI-Jacobi method, and to the more recently…

Instrumentation and Methods for Astrophysics · Physics 2015-05-13 F. Paletou , E. Anterrieu

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…

Numerical Analysis · Mathematics 2021-09-06 Davod Khojasteh Salkuyeh

We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…

Numerical Analysis · Mathematics 2020-09-16 Murat Manguoglu , Volker Mehrmann

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

Optimization and Control · Mathematics 2026-05-05 Xuemei Chen , Owen Deen

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver…

Numerical Analysis · Mathematics 2010-04-27 Matthew Dixon , Zhaojun Bai , Charles Brush , Francis Chung , Emin Dogrul , Tariq Kadir

The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As…

Numerical Analysis · Mathematics 2014-10-14 Cheng-yi Zhang , Shuanghua Luo , Zongben Xu

The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…

Numerical Analysis · Mathematics 2025-04-08 Andy Wathen

Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…

Numerical Analysis · Mathematics 2019-07-08 Ashish Kumar Nandi , Jajati Keshari Sahoo , Debasisha Mishra

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…

Machine Learning · Computer Science 2025-01-14 Jihao Andreas Lin , Shreyas Padhy , Bruno Mlodozeniec , Javier Antorán , José Miguel Hernández-Lobato

This paper considers the numerical solution of generalized Sylvester matrix equations, which arise in many scientific and engineering applications but remain challenging to solve efficiently, particularly when the coefficient matrices are…

Numerical Analysis · Mathematics 2026-04-20 Hongjia Chen , Chun-Hua Zhang , Zhongming Teng , Lei Du

We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…

Optimization and Control · Mathematics 2026-03-16 Henrik Eisenmann , Tasuku Soma , Xun Tang , André Uschmajew