Chapter 6

Multipoint methods with memory

In this chapter we study multipoint methods with memory, a task which is very seldom considered in the literature in spite of high computational efficiency of this kind of root-solvers. Most of these methods are modifications of multipoint methods without memory with optimal order of convergence, studied in the previous chapters. Using two new approaches for calculating a self-correcting parameter, a “sliding” secant-technique and Newton’s interpolation with divided differences, extremely fast convergence of new methods with memory is attained without additional function evaluations. As a consequence, these multipoint methods possess a very high computational efficiency.

Other type of multipoint methods ...

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