Abstract
Let ϕ be analytic iterative vector function with fixed point α and integer order p > 1. It is proved that for each approximation z 0 of α and enough close to α the corresponding iterative process z k + 1=ϕ(z k) converges to α with order p. Using this result we give new shorter proofs for convergence of some well known iterative methods and of iterative methods proposed by authors for solving of nonlinear equations and systems of equations.
This work was supported by Shumen University under contract N 13/2004.
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Nedzhibov, G., Petkov, M. (2005). On Analytic Iterative Functions for Solving Nonlinear Equations and Systems of Equations. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_52
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DOI: https://doi.org/10.1007/978-3-540-31852-1_52
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