Multiplicative preconditioning is a popular tool for handling linear systems of equations provided the relevant information about the associated singular values is available. We propose using additive preconditioners, which are readily available for both general and structured ill conditioned input matrices and which preserve matrix structure. We introduce primal and dual additive preconditioni...

OBJECTIVES Ischemia-reperfusion injury (IRI) is a major cause of acute kidney injury and chronic kidney disease. Two promising preconditioning methods for the kidney, intermittent arterial clamping (IC) and treatment with the hypoxia mimetic cobalt chloride, have never been directly compared. Furthermore, the protective efficacy of the chemically related transition metal Zn2+ against renal IRI ...

We apply our recent preconditioning techniques to the solution of linear systems of equations and computing determinants. We combine these techniques with the Sherman–Morrison–Woodbury formula, its new variations, aggregation, iterative refinement, and advanced algorithms that rapidly compute sums and products either error-free or with the desired high accuracy. Our theoretical and experimental...

In this work we consider preconditioned iterative solution methods for numerical simulations of multiphase flow problems, modelled by the Cahn-Hilliard equation. We focus on the construction and efficiency of various preconditioning techniques and the effect of two discretization methods – conforming and non-conforming finite elements spaces – on those techniques.

Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational they arise symmetric (generalized) eigenvalue problems, nonlinear electronic structures computations, to name a few problems. In statistics machine learning, arise, for various dimensionality reduction techniques such as canonical correlation...

Discretization and linearization of the steady-state Navier-Stokes equations gives rise to a nonsymmetric indeenite linear system of equations. In this paper, we introduce preconditioning techniques for such systems with the property that the eigenvalues of the preconditioned matrices are bounded independently of the mesh size used in the discretization. We connrm and supplement these analytic ...

A multi-level preconditioned iterative method based on a multi-level block ILU factoriza-tion preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coef-cient matrices usually have several rows with zero diagonal values that may cause stability diiculty in standard ILU factoriza...

This paper deals with solving a class of three-by-three block saddle point problems. The systems are solved by preconditioning techniques. Based on an iterative method, we construct upper triangular preconditioner. convergence the presented method is studied in details. Finally, some numerical experiments given to demonstrate superiority proposed preconditioner over existing ones.

We discuss preconditioning and overlapping of waveform relaxation methods for sparse linear diierential systems. It is demonstrated that these techniques signiicantly improve the speed of convergence of the waveform relaxation iterations resulting from application of various modes of block Gauss-Jacobi and block Gauss-Seidel methods to diierential systems. Numerical results are presented for li...