Titlebook: New Developments of Newton-Type Iterations for Solving Nonlinear Problems; Tugal Zhanlav,Ochbadrakh Chuluunbaatar Textbook 2024 The Editor

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Newton-Type Iterations, Convergence and Accelerationsr . on the convergence of the method is studied, and the .-region of convergence is given. The semilocal convergence theorem for CANM is proved using a technique consisting of a new system of recurrence relations. A close relationship between the inexact Newton’s method and CANM is revealed. Based o

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New Developments and Extensions of Newton-Type Methodsese parameters allows increasing the convergence order. Necessary and sufficient conditions for the convergence of Newton-type iterations are suggested. The convergence order of any existing methods can be established using the proposed sufficient condition. Moreover, these conditions allow construc

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Higher Order Newton-Type Iterationsces. Based on these conditions, we developed new multi-parametric higher-order Jarratt and Newton-type iterations with different selections of parameters and implementation algorithms. The proposed family methods include some well-known methods as special cases. Some of the proposed iterative method

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High-Order Derivative-Free Newton-Type Iterationsntroduced. As in Chap. ., the necessary and sufficient convergence conditions are written in terms of parameters. The two parametric families of derivative-free iterations include some well-known methods as particular cases. We also discuss the computational cost of the considered methods and select

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Newton-Type Iterations for Solving Some Problems in Linear Algebranvergence of iteration processes with optimal iteration parameters is proved. The considered algorithms are also applied to a generalized eigenvalue problem with real- or complex-valued symmetric matrices and to a nonlinear eigenvalue problem.