The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s met...The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.展开更多
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 establ...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.展开更多
Smale operator classes of any order for nonlinear operators in Banach space are introduced. For an operator f in Smale operator class of order k , a proper condition for the convergence and the exact estimations error...Smale operator classes of any order for nonlinear operators in Banach space are introduced. For an operator f in Smale operator class of order k , a proper condition for the convergence and the exact estimations error for the iteration of Halley’s family H n j,k ∞ n=0 (1≤j≤k) are given. This Halley’s family is a higher order explicit generalization of Newton iteration.展开更多
文摘The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrual Science Foundation.
文摘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.
文摘Smale operator classes of any order for nonlinear operators in Banach space are introduced. For an operator f in Smale operator class of order k , a proper condition for the convergence and the exact estimations error for the iteration of Halley’s family H n j,k ∞ n=0 (1≤j≤k) are given. This Halley’s family is a higher order explicit generalization of Newton iteration.
