Related papers: Preconditioned GSOR iterative method for a class o…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…
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…