In this paper, we first construct a preconditioned two-parameter generalized Hermitian and skew-Hermitian splitting (PTGHSS) iteration method based on the two-parameter generalized Hermitian and skew-Hermitian splitting (TGHSS) iteration method for non-Hermitian positive definite linear systems. Then a class of PTGHSSbased iteration methods are proposed for solving weakly nonlinear systems base...

In a previous paper, we introduced a coordinate-splitting (CS) form of the equations of motion for multibody systems which together with a modiied nonlinear iteration (CM), is particularly eeective in the solution of certain nonlinear highly oscillatory systems. In this paper, we examine the convergence of the CS and CM iterations and explain the improved convergence of the CM iteration. An exa...

In this paper, we focus on the application of the Peaceman-Rachford splitting method (PRSM) to a convex minimization model with linear constraints and a separable objective function. Compared to the Douglas-Rachford splitting method (DRSM), another splitting method from which the alternating direction method of multipliers originates, PRSM requires more restrictive assumptions to ensure its con...

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Ca...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...

in this paper, we will present a modification of the preconditioned aor-type method for solving the linear system. a theorem is given to show the convergence rate of modification of the preconditioned aor methods that can be enlarged than the convergence aor method.

in this paper, we present a new iterative method with order of convergence eighth for solving nonlinear equations. periteration this method requires three evaluations of the function and one evaluation of its first derivative. a general error analysis providing the eighth order of convergence is given. several numerical examples are given to illustrate the efficiency and performance of the new ...

We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterative method. For example, the standard GPBi-CG algorithm itself can be used as a preconditioner, as can other Krylov subspace methods or splitting methods. Numerical e...