For the nonlinear system $$x=g(x)+h(x)+c, x\in R^n,$$ where $g$ and $h$ are isotone and antitone mappings respectively, a two-sided interval iterative method is presented, the initial condition of the two-sided iterative method is relaxed, and the convergence of the two methods are proved.

It is well known that the $x$-condition number of a linear operator is a measure of ill condition with respect to its generalized inverses and a relative error bound with respect to the generalized inverses of operator $T$ with a small perturbation operator E, namely,$$\frac{\|(T+E)^+-T^+\|}{\|T^+\|}\leq \frac{x(T)\frac{\|E\|}{\|T\|}}{1-x(T)\frac{\|E\|}{\|T\|}},$$ where $x{T}=\|T\|\dot\|T^+\|$. The problem is whether there exists a positive number $μ(T)$ independent of $E$ but dependent on $T$ such that the above relative error bound holds and $μ(T)＜x(T)$.
In this paper, an answer is given to this problem.

In this paper we present an interior point method which solves a linear programming problem by using an affine transformation. We prove under certain assumptions that the algorithm converges to an optimal solution even if the dual problem is degenerate as long as the prime is bounded, or to a ray direction if the optimal value of the objective function is unbounded.

L. R. Fletcher has pointed out that how to best exploit any freedom of choice in regard to the eigenvalues of a closed-loop system is an unsolved problem for robust pole assignment in control system design. This paper suggests a numerical method to solve this problem. Numerical results show that the method is feasible.  

The distance between two neighbouring multivariate Bézier nets is proved to be $O(m^{-2})$ in this paper. As a consequence, the sequence of Bézier nets is uniformly convergent with the optimal approximation order $O(m^{-1})$. Furthermore, the structures of Bézier nets are explored by investigating how the piecewise linear surface tends to the Bézier surface of $C^{\infty}$.