Multi-step nonlinear ABS methods and their efficiency analysis
type: Item
instance of: scholarly article
title: Multi-step nonlinear ABS methods and their efficiency analysis
zbMATH Open document ID: 0728.65042
DOI: 10.1007/BF02239168
author: Zhijian Huang
published in: Computing
publication date: 1991-01-01T00:00:00Z
review text: The multi-step principle developed 20 years ago for Newton's method and most of its discretized versions is applied to nonlinear ABS methods. In the multi-step methods each major iteration step consists of \(m+1\) minor iterations where the derivative information is fixed and only function values are to be computed. The method is shown to converge locally with O-order \(m+2\), and for given dimension n the optimal step number m which minimizes an asymptotic measure of complexity is determined.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 4203588
zbMATH Keywords: nonlinear ABS methods
zbMATH Keywords: multi-step methods
zbMATH Keywords: measure of complexity
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02239168
OpenAlex ID: W402121114
description: scientific article; zbMATH DE number 4203588