Displaying similar documents to “What should be a rate of convergence ?”

How to increase convergence order of the Newton method to 2 × m ?

Sanjay Kumar Khattri (2014)

Applications of Mathematics

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We present a simple and effective scheme for forming iterative methods of various convergence orders. In this scheme, methods of various convergence orders, such as four, six, eight and ten, are formed through a modest modification of the classical Newton method. Since the scheme considered is a simple modification of the Newton method, it can be easily implemented in existing software packages, which is also suggested by the presented pseudocodes. Finally some problems are solved, to...

An application of the induction method of V. Pták to the study of regula falsi

Florian-Alexandru Potra (1981)

Aplikace matematiky

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In this paper we introduce the notion of " p -dimensional rate of convergence" which generalizes the notion of rate of convergence introduced by V. Pták. Using this notion we give a generalization of the Induction Theorem of V. Pták, which may constitute a basis for the study of the iterative procedures of the form X n + 1 = F ( x n - p + 1 , X n - p + 2 , ... , x n ) , n = 0 , 1 , 2 , ... . As an illustration we apply these results to the study of the convergence of the secant method, obtaining sharp estimates for the errors at each step of the iterative...