构造m-增生算子方程解的Ishikawa迭代程序

设X是一致光滑Banach空间，T：D（T）∪↓X→X是具闭的定义域D（T）的m-增生算子。不经假设值域R（T）有界与对[0,1]中序列[βn}作任何限制，就表征了用于构造m-增生算子方程x Tx=f的解的具误差的Ishikawa迭代序列的收敛性。而且，若T还是局部Lipschitz算子，则给出了m-增生算子方程x Tx=f的逼近解的误差估计。     

Banach空间中的广义Hη增生算子及其在变分包含中的应用

在Banach空间中,引入和研究了新的广义H-η-增生算子,对广义m-增生算子与H-η-单调算子提供了一个统一的框架．还定义了广义H-η-增生算子相应的预解算子,并且证明了其Lipschitz连续性．作为应用,考虑了涉及广义H-η-增生算子的一类变分包含问题的可解性．利用预解算子方法,构造了一个求解变分包含的迭代算法．在适当假设下,证明了变分包含解的存在性和由算法生成的迭代序列的收敛性．     

含m-增生算子或φ-伪压缩映象具误差的Ishikawa迭代的收敛性问题

主要研究了m-增生算子以及φ-伪压缩映象的分别带两种误差的Ishikawa迭代序列的收敛性问题. 推广了Osilike等人的相关结果.     

扰动m-增生算子方程的Ishikawa迭代程序

设X是光滑Banach空间,A:X→X是一致连续的m-增生算子,S:X→X是一致连续的φ--强增生算子,本文证明实光滑Banach空间上连续的m-增生算子是单值的且具误差的Ishikawa和Mann迭代序列强收敛到方程z=Sx+λAx的唯一解,其中z∈X,λ≥0.我们的结果改进和推广了近期文献中的相应结果.     

含m—增生算子或￠—伪压缩映象具误差的Ishikawa迭代的收敛性问题

主要研究了m-增生算子以及￠-伪压缩映象的分别带两种误差的Ishikawa迭代序列的收敛性问题,推广了Osilike等人的相关结果。     

关于强伪压缩算子与强增生算子的Ishikawa型迭代序列收敛性的特征

本文结果表征了用于构造强增生算子方程解,m-增生算子方程解及强伪压缩算子不动点的(带误差的)Ishikawa型迭代序列的收敛性,推广与改进了Chidume与Osilike的定理1,定理2及定理3(Nonlinear Anal.TMA,1999,36(7):863-872)。     

Banach空间中关于m-增生算子零点的一种新的粘性隐式迭代算法

在Banach空间中研究关于两个逆强增生算子的一般变分不等式问题和m-增生算子零点的粘性隐式迭代算法,对参数的适当限制下,利用超梯度方法,得到了若干强收敛定理,推广和改进了其他相关作者的主要结果.     

关于增生算子方程解的带误差的Ishikawa迭代程序

该文在Banach空间中证明了，带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解．而且，也给Ishikawa迭代序列提供了一般的收敛率估计．利用该结果还推得，带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解．     

Banach空间中有限个增生算子公共零点的带误差的迭代格式

本文研究了有限个增生算子公共零点的迭代构造,利用非扩展保核收缩映射的性质,在满足Opial条件或其范数是Frech閠可微的实一致凸Banach空间中,获得上迭代序列弱收敛于有限个增生算子公共零点的结论.对单个增生算子推广到了有限个的情形.     

关于增生算子方程解的Ishikawa迭代逼近

设X是任意实Banach空间,T:X→X是Lipschitz连续的增生算子.本文证明了,带误差的Ishikawa迭代序列强收敛到方程x Tx=f的唯一解.而且,还给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果,本文推得,若T:X→X是Lipschitz连续的强增生算子,则带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解.     

On the simultaneous determination of the zeros of an analytic function inside a simple smooth closed contour in the complex plane

A family of higher-order iterative methods for the simultaneous determination of all simple or multiple zeros of an analytic function (inside a simple smooth closed contour) is obtained using earlier results of the author. With the help of circular arithmetic, the interval variant of this family is proposed. Many parallel iterative methods of the literature are special cases of this family.     

Safe convergence of simultaneous methods for polynomial zeros

The theory of point estimation treating the initial conditions for the safe convergence of iterative processes for the simultaneous determination of polynomial zeros is considered. A general approach which makes use of corrections appearing in iterative formulas is given and demonstrated in the case of three well known methods without derivatives and based on Weierstrass’ corrections. The established convergence conditions are of practical importance since they depend only on available data: coefficients of a polynomial and initial approximations to the zeros. This revised version was published online in June 2006 with corrections to the Cover Date.     

An automatic search procedure for finding real zeros

Summary The paper describes the implementation of a globally convergent iterative algorithm for determining all the real zeros of certain classes of functions in any given interval. The algorithm is developed in terms of Ostrowski's square root formula and in the case of polynomials the relation with Laguerre's formula is obtained. A device is incorporated for overcoming the problem of numerical instability together with a number of associated devices for ensuring that no zeros have been missed. Application of the method is illustrated by two examples having clustered zeros.     

Practical Band Toeplitz Preconditioning and Boundary Layer Effects

In the last decade many efficient iterative solvers for n×n Hermitian positive definite Toeplitz systems have been devised. Many of them are based on band Toeplitz preconditioners: they are optimal but require the knowledge of the zeros of the underlying generating function. In some cases this information is available and in some cases is not. In [27] an economic numerical procedure for finding these zeros within a given precision has been devised. Here we provide conditions on the approximation error of these zeros in order to maintain the optimality that is a convergence rate independent of the dimension n of the considered linear systems.     

Banach空间中m-d-增生算子零点迭代算法的构造

研究了Banach空间中m-d-增生算子零点的迭代算法的构造问题,获得了一个强收敛定理.     

逼近拟增生算子零点的大范围收敛定理

研究了一致光滑Banach空间中拟增生算子零点的迭代逼近问题,获得了一个大范围收敛定理,改进了许多已知的结果.     

On the steepest descent approximation method for the zeros of generalized accretive operators

In this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of Reich [S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978) 85–92] and given results extend and improve some of the earlier results which include the steepest descent approximation method.     

Further investigation on iteration processes for pseudocontractive mappings with application

A new iterative method for approximating fixed points of bounded and continuous pseudocontractive mapping is proposed and a strong convergence theorem is obtained. As an application, we prove that a slight modification of our new scheme could be employed for approximating zeros of bounded and continuous accretive operators. Our theorems extend and unify most of the results that have been proved for this class of mappings.     

Weierstrass formula and zero-finding methods

Summary. Classical Weierstrass' formula [29] has been often the subject of investigation of many authors. In this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions. We are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros. Conditions for the safe convergence of Weierstrass' method, depending only on initial approximations, are given. In particular, we study polynomials with interval coefficients. Using an interval version of Weierstrass' method enclosures in the form of disks for the complex-valued set containing all zeros of a polynomial with varying coefficients are obtained. We also present Weierstrass-like algorithm for approximating, simultaneously, all zeros of a class of analytic functions in a given closed region. To demonstrate the proposed algorithms, three numerical examples are included. Received September 13, 1993