Timeline for Multi-variate secant method for solving $F(x)=0$
Current License: CC BY-SA 2.5
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| Dec 20, 2018 at 13:30 | history | edited | Federico Poloni |
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| Oct 13, 2010 at 5:21 | comment | added | Denis Serre | @Gjergji. This is clear and it answers my question. Thanks to Wadim for having pointed the reference. I have asked our library to purchase the book. | |
| Oct 12, 2010 at 23:33 | comment | added | Gjergji Zaimi | On page 198 of Ortega-Rheinboldt it says "Although the $n+1$-point sequential secant method requires the least amount of computation per step, it will be shown in Chapter 11 that the method is prone to unstable behavior and that no satisfactory convergence results can be given. In contrast, the two-point methods will be shown to retain the essential properties of Newton's method and, in particular, satisfactory local convergence theorems will be obtained for them in section 11.2". Chapters 9-11 are devoted to convergence and local convergence theorems for various iterative processes. | |
| Oct 12, 2010 at 12:58 | comment | added | Denis Serre | I do not have access to this book (actually a reprint of a 1970 edition) here. Google scholar provides some scattered pages, which leave me uncomfortable whether the book really deals with this version of secant method. I'll come back when I know more about this. | |
| Oct 12, 2010 at 11:38 | comment | added | Wadim Zudilin | It seems that the book [J. Ortega and W. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, SIAM, Philadelphia, PA, 2000] (avaliable at google books) discusses the multivariate method. | |
| Oct 12, 2010 at 11:29 | history | asked | Denis Serre | CC BY-SA 2.5 |