| It is well known that ordering of unknowns greatly a ects convergence in Incomplete LU (ILU) factorization preconditioned iterative methods. The authors recently proposed a simple evaluation way for orderings in ILU preconditioning. The evaluation index, which has a simple relationship with a norm of a remainder matrix, is easily computed without additional memory requirement. The computation...

The improvement in AOR method for solving this system has been carried out by Hadjimos [1], Recently, Yao-Tang et al. [2], improved AOR method which has been developed by [1]. In this work, we construct a preconditioner to improve the Accelerated Over-relaxation (AOR) iterative method for solution of linear systems. We reduce the spectral radius of iterative matrix by multiplication of Precondi...

This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New (NSGS), and Parametric (PSGS) methods for solving linear system Ax = b are considered. is precondition type I + S. Convergence properties analyzed standard procedures a numerical experiment undertaken to compare efficiency matrix. Algorithms prepared. MATLAB software used checking computational itera...

In this paper‎, ‎an efficient dropping criterion has been used to compute the IUL factorization obtained from Backward Factored APproximate INVerse (BFAPINV) and ILU factorization obtained from Forward Factored APproximate INVerse (FFAPINV) algorithms‎. ‎We use different drop tolerance parameters to compute the preconditioners‎. ‎To study the effect of such a dropping on the quality of the ILU ...

Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using nonassembled matrices from discretized partial differential equations (PDEs). Therefore, DD were mainly successful when solving systems stemming PDEs. In paper, we present fully algeb...

Challenges in Robotics motivate the problem of solving a system of the form AAx = A b, where the matrix A has at most two nonzero arbitrary entries (reals or block matrices) in each row. There is a lot of interest in solving these kind of systems efficiently, which correspond to the errors in ”measurements” of the position of the robot while it moves in the 3-D space, so this problem has lots o...

We consider a family of symmetric matrices Aω = A0 +ωB, with a nonnegative definite matrix A0, a positive definite matrix B, and a nonnegative parameter ω ≤ 1. Small ω leads to a poor conditioned matrix Aω with jumps in the coefficients. For solving linear algebraic equations with the matrix Aω, we use standard preconditioned iterative methods with the matrix B as a preconditioner. We show that...