The paper discusses $H$-splitting and $H$-compatible splitting, furthermore, some properties are given. Asynchronous parallel multisplitting algorithm and its generalization for linear systems $Ax=b$ are established. Convergence of these algorithms is proved under given conditions. The convergent range of relaxation factor $\omega$ is given, numerical example is shown.

A Legendre pseudospectral scheme is proposed for solving initial-boundary value problem of nonlinear Klein-Gordon equation. The numerical solution keeps the discrete conservation. Its stability and convergence are investigated. Numerical results are also presented, which show the high accuracy. The technique in the theoretical analysis provides a framework for Legendre pseudospectral approximation of nonlinear multi-dimensional problems.

In this work, the vortex methods for Euler equations with initial boundary value problem is considered, Poisson equations are solved using boundary element methods which can be seen to require less operations to compute the velocity field from the vorticity by Chorin$^{[6]}$. We prove that the rate of convergence of the boundary element schemes can be independent of the vortex blob parameters.

RQI is an approach for eigenvectors of matrices. In 1974, B.N Parlett proved that it was a "successful algorithm" with cubic convergent speed for normal matrices. After then, several authors developed relevant theory and put this research into dynamical frame. [3] indicated that RQI failed for non-normal matrices with complex eigenvalues.
In this paper, RQI for non-normal matrices with only real spectrum is analyzed. The authers proved that eigenvectors are super-attractive fixed points of RQI. The geometrical and topological behaviours of two periodic orbits are considered in detail.
The existence of three or higher periodic orbits and their geometry are considered in detail.
The existence of three or higher periodic orbits and their geometry are still open and of interest. It will be reported in our forthcoming paper.  

Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of $C^1$ discrete tetrahedral interpolants with only $C^1$ data required. As special cases of the class characterized, we give two $C^1$ discrete tetrahedral interpolants which have concise expressions.

The stability in $L^\infty$-norm is considered for the Ritz-Volterra projection and some applications are presented in this paper. As a result, point-wise error estimates are established for the finite element approximation for the parabolic integro-differential equation, Sobolev equations, and a diffusion equation with non-local boundary value problem.

In this paper, an SQP type algorithm with a new nonmonotone line search technique for general constrained optimization problems is presented. The new algorithm does not have to solve the second order correction subproblems for each iterations, but still can circumvent the so-called Maratos effect. The algorithm's global convergence and superlinear convergent rate have been proved. In addition, we can prove that, after a few iterations, correction subproblems need not be solved, so computation amount of the algorithm will be decreased much more. Numerical experiments show that the new algorithm is effective.