Communication-hiding pipelined BiCGSafe methods for solving large linear systems

The communication-hiding pipelined BiCGstab method for the parallel solution of large unsymmetric linear systems

A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov subspace methods for large and sparse linear systems. The typical synchronization bottleneck is mitigated by overlapping time-consuming global communication phases with local computations in the algori...

Solving large systems arising from fractional models by preconditioned methods

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Defuzzification method for solving fuzzy linear systems

A Proposal of Variants of BiCGSafe Method for Solving Linear Systems in Realistic Problems

We consider on efficient and stable solution for linear systems by product-type iterative methods. By means of improvement on ordering of Lanczos and stability polynomials which construct algorithm of product-type BiCG method, we derive new algorithm based on BiCGSafe method with safety convergence. We will apply the proposed BiCGSafe method to solve linear systems which appeared in a variety o...