Solving large tomographic linear systems: size reduction and error estimation

Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems

IDR(s) is one of the most efficient methods for solving large sparse nonsymmetric linear systems of equations. We present two useful extensions of IDR(s), namely a flexible variant and a multi-shift variant. The algorithms exploit the underlying Hessenberg decomposition computed by IDR(s) to generate basis vectors for the Krylov subspace. The approximate solution vectors are computed using a Qu...

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

Reduction algorithms for solving large systems of logical equations

Large systems of logical equations are considered in this paper, each depending on a restricted number of variables. A method of reduction is suggested that reduces the number of roots in separate equations, which in its turn saves time spent for finding roots of the whole system. Three mechanisms of reduction are proposed, each looking for some prohibited combinations of variables in separate ...

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...