Some reflections on Newton's method

F. Twilt

doi:10.1007/978-94-011-1814-9_8

Some reflections on Newton's method

F. Twilt

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

Abstract

An infinitesimal version (Newton flow) of Newton’s iteration for finding zeros of rational functions on the complex plane is introduced. Structural stability aspects are discussed, including a characterization and classification of structurally stable Newton flows in terms of certain plane graphs. Possible generalizations to other classes of functions are indicated and several open problems are posed.

Original language	English
Title of host publication	Topics in Engineering Mathematics
Subtitle of host publication	Modeling and Methods
Editors	Adriaan van der Burgh, Juriaan Simonis
Publisher	Kluwer Academic Publishers
Pages	217-237
ISBN (Electronic)	978-94-011-1814-9
ISBN (Print)	978-94-010-4800-2
DOIs	https://doi.org/10.1007/978-94-011-1814-9_8
Publication status	Published - 1992

Publication series

Name	Mathematics and Its Applications
Publisher	Kluwer Academic Publishers
Volume	81

Keywords

METIS-140991
Newton flow
structural stability
rational function

Access to Document

10.1007/978-94-011-1814-9_8

Cite this

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abstract = "An infinitesimal version (Newton flow) of Newton{\textquoteright}s iteration for finding zeros of rational functions on the complex plane is introduced. Structural stability aspects are discussed, including a characterization and classification of structurally stable Newton flows in terms of certain plane graphs. Possible generalizations to other classes of functions are indicated and several open problems are posed.",

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AB - An infinitesimal version (Newton flow) of Newton’s iteration for finding zeros of rational functions on the complex plane is introduced. Structural stability aspects are discussed, including a characterization and classification of structurally stable Newton flows in terms of certain plane graphs. Possible generalizations to other classes of functions are indicated and several open problems are posed.

KW - METIS-140991

KW - Newton flow

KW - structural stability

KW - rational function

U2 - 10.1007/978-94-011-1814-9_8

DO - 10.1007/978-94-011-1814-9_8

M3 - Chapter

SN - 978-94-010-4800-2

T3 - Mathematics and Its Applications

SP - 217

EP - 237

BT - Topics in Engineering Mathematics

A2 - van der Burgh, Adriaan

A2 - Simonis, Juriaan

PB - Kluwer Academic Publishers

ER -

Some reflections on Newton's method

Abstract

Publication series

Keywords

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