数值分析学习笔记(1)- Big O & rate of convergence 收敛速度 数值分析学习笔记(2)- 方程求解:Bisection method 二分法 & Fixed-point iteration 不动点迭代 数值分析学习笔记(3)- 方程求解:牛顿迭代法Newton method & 弦截法 Secant Method与收敛阶Converge Order 数值分析学习笔记(4)- 插值:拉格朗日插值法Lagra...
It is found that the usual invertibility and smoothness assumptions on the Frechet derivative g'(x) are sufficient for local and linear but not necessarily superlinear convergence of secant methods. For both Broyden's Method and Variable Metric Methods it is shown that the asymptotic rate of ...
Standard text books in numerical analysis state that the secant method is superlinear: the rate of convergence is set by the gold number. Nevertheless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes ...
128A_Sec1.3_Part2-Rate_of_Convergence 10:29 128A_Sec2.1_Part1-Bisection_Method 09:01 128A_Sec2.1_Part2-MATLAB_Demo 09:28 128A_Sec2.1_Part3-Convergence 08:55 128A_Sec2.2_Part1-Fixed_Points 10:43 128A_Sec2.2_Part2-Existence_Uniqueness_Proof 11:07 128A_Sec2.2_Part3-Fixed...
Moreover, an error estimate is provided which matches the convergence order of the method.doi:10.1016/j.amc.2006.09.111Hongmin RenQingbiao WuElsevier Inc.Applied Mathematics & ComputationRen, H., Wu, Q.: Convergence ball of a modified secant method with convergence order 1.839... Appl. Math...
Torregrosa, On the convergence of a damped secant method with modified right-hand side vector, Applied Mathematics and Computation 252 (2015) 315-323.I.K. Argyros, A. Cordero, A.A. Magrenan, J.R. Torregrosa, On the convergence of a Damped Secant method with modified right-hand side ...
In this paper, we show that the main results of the local convergence theory for least-change secant update methods of Dennis and Walker (SIAM J. Numer. Anal. 18 (1981), 949-987) can be proved using the theory introduced recently by Martinez (Math. Comp. 55 (1990), 143-167). In ...
Moreover, the R-linear convergence rate of the modified HS method is established. Preliminary numerical results show that the proposed method is promising, and competitive with the well-known CG-DESCENT method.Zhifeng DaiFenghua WenNumerical Algorithms...
of a given matrix.The global and superlinear convergence of the method is proved under specifically initialized matrices.The numerical examples are also provided.And a comparison is done between the secant method and the Newton method.It is shown that the secant method is an effective numerical ...
940]. The convergence of (Bk) is for example of interest because it is closely related to the rate of convergence of (uk), see, e.g., Lemma 2 and 3. For invertible F′(u¯), there is only one result available: It is established in [22, Theorem 5.7] and in [17] that if ...