THE ERROR ESTIMATES OF HALLEY'S METHOD

In this paper we give an almost sharp error estimate of Halley's iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley's iteration in Banach spaces.  

Minimizing a differentiable function over a differential manifold

To generalize the descent methods of unconstrained optimization to the constrained case, we define intrinsically the gradient field of the objective function on the constraint manifold and analyze descent methods along geodesics, including the gradient projection and reduced gradient methods for special choices of coordinate systems. In particular, we generalize the quasi-Newton methods and establish their superlinear convergence; we show that they only require the updating of a reduced size matrix. In practice, the geodesic search is approximated by a tangent step followed by a constraints restoration or by a simple arc search again followed by a restoration step.A first draft of this paper was first presented at the 10th International Symposium on Mathematical Programming, Montreal, Canada, 1979. The present version has been prepared while the author was visiting the Department of Engineering-Economic Systems at Stanford University, partially supported by AFOSR Grant No. 77-3141.  

一致凸Banach空间非扩张映像具误差的Ishikawa迭代

研究一致凸 Banach空间中非扩张映像迭代序列的收敛问题 ,使用了基于 Ishikawa迭代的一种具误差的 Ishikawa迭代 ,证明了非扩张映像的具误差的 Ishikawa迭代收敛定理 .  

一类非线性算子Ishikawa迭代序列的强收敛定理

使用新的分析技巧，研究了一致光滑Ｂａｎａｃｈ空间中φ 强增生算子方程的解和φ 强伪压缩算子不动点的Ｉｓｈｉｋａｗａ迭代逼近问题，改进和扩展了近期的许多相关结果．  

区间值函数和Fuzzy值函数的积分收敛

本文在[1]的基础上,定义了区间值函数与Fuzzy值函数的积分,给出有关积分收敛的一些结果。  

On Halley-type iterations with free second derivative

In this paper, we relax the convergence conditions required in Ezquerro and Hernández (Int. J. Pure Appl. Math. 6(1) (2003) 103) for a multipoint third-order iteration of Halley type, where the conditions provided are the known ones for methods of order three.  

关于任意随机适应序列部分和的一类局部极限定理

研究任意随机适应序列部分和的一类局部极限定理,推广了最近发表的几个结果．  

B值随机变量序列的局部收敛定理

本文的目的是研究B值随机变量序列的局部收敛定理。作为推论，得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。  

模糊值Choquet积分(Ⅱ)--函数关于模糊值模糊测度的Choquet积分

研究一种取值于模糊数集的Choquet积分，该积分的被积函数是单值函数，所用的测度是模糊值模糊测度。给出其定义、性质和收敛定理。  

Choquet积分的收敛定理

Murofushi、Sugeno等学者已对关于模糊测度的Choquet积分进行了详细的研究，但关于积分的收敛理论是不够的。本文讨论这一问题，给出Choquet积分的一些收敛定理，包括广义单调收敛定理、Fatou引理等。从中可以看出，Choquet积分与Sugeno模糊积分具有相同的收敛定理。