In this paper, we discuss convergence of the extrapolated iterative methods for solving singular linear systems. A general principle of extrapolation is presented. The semiconvergence of an extrapolated method induced by a regular splitting and a nonnegative splitting is proved whenever the coe cient matrix A is a singular M -matrix with ‘property c’ and an irreducible singular M -matrix, respe...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

We describe a highly flexible framework to solve 3D radiation transfer problems in scattering dominated environments based on a long characteristics piecewise parabolic formal solution and an operator splitting method. We find that the linear systems are efficiently solved with iterative solvers such as Gauss-Seidel and Jordan techniques. We use a sphere-in-a-box test model to compare the 3D re...

Climent and Perea [Journal of Computational Applied Mathematics 58:43–48, 2003; MR2013603] proposed first the convergence theory two-stage iterative scheme for solving real rectangular linear systems. In this article, we revisit same theory. The main result provides some sufficient conditions which guarantee that induced splitting from a is proper weak regular splitting. We then establish few c...

Incremental closure is a proof search technique for free variable analytic tableaux where partial solutions are updated along with tableaux expansion. In this paper we address possible adaptations of the incremental closure technique to variable splitting tableaux. Variable splitting tableaux provide a sound way to instantiate occurrences of the same variable in different branches differently b...

‎in this article‎, ‎we introduce a new type iterative scheme for‎ ‎approximating common fixed points of two asymptotically‎ ‎nonexpansive mappings is defined‎, ‎and weak and strong convergence‎ ‎theorem are proved for the new iterative scheme in a uniformly‎ ‎convex banach space‎. ‎the results obtained in this article‎ ‎represent an extension as well as refinement of previous known‎ ‎resu...

Computation of the Cramer-Rao bound (CRB) on estimator variance requires the inverse or the pseudo-inverse Fisher information matrix (FIM). Direct matrix inversion can be computationally intractable when the number of unknown parameters is large. In this correspondence, we compare several iterative methods for approximating the CRB using matrix splitting and preconditioned conjugate gradient al...