‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎‎direct iteration methods for solving a linear system where the‎‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎‎rank linear equations‎, ‎w...

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...

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

This paper has been devoted to apply the Reconstruction of Variational Iteration Method (RVIM) to handle the systems of integro-differential equations. RVIM has been induced with Laplace transform from the variational iteration method (VIM) which was developed from the Inokuti method. Actually, RVIM overcome to shortcoming of VIM method to determine the Lagrange multiplier. So that, RVIM method...