【摘要】 从带一个参数的三阶迭代族(其中包括Halley迭代,Chebyshev迭代和超Halley迭代)出发,推出避免二阶导数计算的带两个参数的迭代族.在Newton-Kantorovich型的假设条件下,通过用一个递推关系证明了此迭代族的三阶收敛性,并给出了非线性算子方程解的存在惟一性定理.更多还原

【Abstract】 A family of iterations with two parameters which can avoid the computation of the second Frechet-derivative is introduced.Using Newton-Katorovih-type assumption,a convergent theorem for the family of iterations is established,and the result on the existence of a unique solution to the nonlinear equation is given by using a technique based on a new system of recurrence relations.更多还原