Directional halley and quasi-halley methods in N variables

Yuri Levin; Adi Ben-Israel

doi:https://doi.org/10.1016/S1570-579X(01)80021-5

Directional halley and quasi-halley methods in N variables

Yuri Levin, Adi Ben-Israel

Rutgers Business School, Management & Information Systems

Rutgers, The State University

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

A directional Halley method for functions f of n variables is shown to converge, at a cubic rate, to a solution. To avoid the second derivative needed in the Halley method we propose a directional quasi-Halley method, with one more function evaluation per iteration than the directional Newton method, but with convergence rates comparable to the Halley method.

Original language	English (US)
Title of host publication	Studies in Computational Mathematics
Publisher	Elsevier
Pages	345-367
Number of pages	23
Edition	C
DOIs	https://doi.org/10.1016/S1570-579X(01)80021-5
State	Published - 2001

Publication series

Name	Studies in Computational Mathematics
Number	C
Volume	8

ASJC Scopus subject areas

Computational Mathematics

Access to Document

https://doi.org/10.1016/S1570-579X(01)80021-5

Cite this

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abstract = "A directional Halley method for functions f of n variables is shown to converge, at a cubic rate, to a solution. To avoid the second derivative needed in the Halley method we propose a directional quasi-Halley method, with one more function evaluation per iteration than the directional Newton method, but with convergence rates comparable to the Halley method.",

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AB - A directional Halley method for functions f of n variables is shown to converge, at a cubic rate, to a solution. To avoid the second derivative needed in the Halley method we propose a directional quasi-Halley method, with one more function evaluation per iteration than the directional Newton method, but with convergence rates comparable to the Halley method.

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M3 - Chapter

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Directional halley and quasi-halley methods in N variables

Abstract

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ASJC Scopus subject areas

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