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Multipoint Methods for Solving Nonlinear Equations

Miodrag S. Petković, Beny Neta, Ljiljana D. Petković, and Jovana Dzunic
Publisher: 
Elsevier
Publication Date: 
2013
Number of Pages: 
299
Format: 
Hardcover
Price: 
129.95
ISBN: 
9780123972989
Category: 
Monograph
We do not plan to review this book.

1 Basic concepts
 1.1 Classification of iterative methods
 1.2 Order of convergence
 1.3 Computational efficiency of iterative methods
 1.4 Initial approximations
 1.5 One-point iterative methods for simple zeros
 1.6 Methods for determining multiple zeros
 1.7 Stopping criterion

2 Two-Point methods
 2.1 Cubically convergent two-point methods
 2.2 Ostrowski’s fourth-order method and its generalizations
 2.3 Family of optimal two-point methods
 2.4 Optimal derivative free two-point methods
 2.5 Kung-Traub’s multipoint methods
 2.6 Optimal two-point methods of Jarratt’s type
 2.7 Two-point methods for multiple roots

3 Three-Point non-optimal methods
 3.1 Some historical notes
 3.2 Methods for constructing sixth-order root-finders
 3.3 Ostrowski-like methods of sixth order
 3.4 Jarratt-like methods of sixth order
 3.5 Other non-optimal three-point methods

4 Three-Point optimal methods
 4.1 Optimal three-point methods of Bi, Wu, and Ren
 4.2 Interpolatory iterative three-point methods
 4.3 Optimal methods based on weight functions
 4.4 Eighth-order Ostrowski-like methods
 4.5 Derivative free family of optimal three-point methods

5 Higher-order optimal methods
 5.1 Some comments on higher-order multipoint methods
 5.2 Geum-Kim’s family of four-point methods
 5.3 Kung-Traub’s families of arbitrary order of convergence
 5.4 Methods of higher-order based on inverse interpolation
 5.5 Multipoint methods based on Hermite’s interpolation
 5.6 Generalized derivative free family based on Newtonian interpolation

6 Multipoint methods with memory
 6.1 Early works
 6.2 Multipoint methods with memory constructed by inverse interpolation
 6.3 Efficient family of two-point self-accelerating methods
 6.4 Family of three-point methods with memory
 6.5 Generalized multipoint root-solvers with memory
 6.6 Computational aspects

7 Simultaneous methods for polynomial zeros
 7.1 Simultaneous methods for simple zeros
 7.2 Simultaneous method for multiple zeros
 7.3 Simultaneous inclusion of simple zeros
 7.4 Simultaneous inclusion of multiple zeros
 7.5 Halley-like inclusion methods of high efficiency

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