Basic concepts. Classification of iterative methods ; Order of convergence ; Computational efficiency of iterative methods ; Initial approximations ; One-point iterative methods for simple zeros ; Methods for determining multiple zeros ; Stopping criterion.
Two-Point methods. Cubically convergent two-point methods ; Ostrowski's fourth-order method and its generalizations ; Family of optimal two-point methods ; Optimal derivative free two-point methods ; Kung-Traub's multipoint methods ; Optimal two-point methods of Jarratt's type ; Two-point methods for multiple roots.
Three-Point non-optimal methods. Some historical notes ; Methods for constructing sixth-order root-finders ; Ostrowski-like methods of sixth order ; Jarratt-like methods of sixth order ; Other non-optimal three-point methods.
Three-Point optimal methods. Optimal three-point methods of Bi, Wu, and Ren ; Interpolatory iterative three-point methods ; Optimal methods based on weight functions ; Eighth-order Ostrowski-like methods ; Derivative free family of optimal three-point methods.
Higher-order optimal methods. Some comments on higher-order multipoint methods ; Geum-Kim's family of four-point methods ; Kung-Traub's families of arbitrary order of convergence ; Methods of higher-order based on inverse interpolation ; Multipoint methods based on Hermite's interpolation ; Generalized derivative free family based on Newtonian interpolation.
Multipoint methods with memory. Early works ; Multipoint methods with memory constructed by inverse interpolation ; Efficient family of two-point self-accelerating methods ; Family of three-point methods with memory ; Generalized multipoint root-solvers with memory ; Computational aspects.
Simultaneous methods for polynomial zeros. Simultaneous methods for simple zeros ; Simultaneous method for multiple zeros ; Simultaneous inclusion of simple zeros ; Simultaneous inclusion of multiple zeros ; Halley-like inclusion methods of high efficiency.
