中心Hlder条件下求解重根的Halley算法的收敛半径

Convergence Radius of Halley's Method for Multiple Roots under Center-Hlder Continuous Condition

鉴于具有积分余项的Taylor展开式的处理方法的简单性和有效性,用该方法来讨论求解重根的Halley算法的收敛半径问题,给出在仅仅假设方程的m+1阶导数满足中心Hlder的条件下Halley算法的收敛半径表达式.文献[6]中已经估算出了Halley算法的收敛半径,但没有给出该方法的优缺点.从数值角度对此结论进行分析,说明两种处理方法的条件和结论的不同.

In terms of the simplicity and effectiveness of the processing approach based on the Taylor expansion with integral remains, in this thesis, we will try to use it to give the estimate of the convergence radius of Halley＇s method for multiple roots. The convergence radius of Halley＇ s method will be given only under the condition that the （m＋l）th derivative of function satisfies center-HtSlder continuous condition. The 6th reference literature has already estimated the con- vergence radius of Halley＇s method, but has not given the advantages and disadvantages of this method. Some numerical tests are also given to verify our theoretical analysis, and show the differences of conditions and conclusions between these two processing approaches.