An Interval Newton Method

R I. Greenberg; Eldon R. Hansen

doi:10.1016/0096-3003(83)90001-2

An Interval Newton Method

R I. Greenberg, Eldon R. Hansen

Department of Computer Science

Lockheed Missiles & Space Company

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.

Original language	American English
Journal	Computer Science: Faculty Publications and Other Works
Volume	12
Issue number	2-3
DOIs	https://doi.org/10.1016/0096-3003(83)90001-2
State	Published - May 1 1983

Keywords

systems of nonlinear equations

Disciplines

Numerical Analysis and Computation
Numerical Analysis and Scientific Computing

Access to Document

10.1016/0096-3003(83)90001-2License: Unspecified

An Interval Newton MethodFinal published version, 4.59 MBLicense: Unspecified

http://dx.doi.org/10.1016/0096-3003(83)90001-2

Cite this

@article{15a6ae3d8fa2431db28ab1bae60e047e,

title = "An Interval Newton Method",

abstract = " We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.",

keywords = "systems of nonlinear equations",

author = "Greenberg, {R I.} and Hansen, {Eldon R.}",

year = "1983",

month = may,

day = "1",

doi = "10.1016/0096-3003(83)90001-2",

language = "American English",

volume = "12",

journal = "Computer Science: Faculty Publications and Other Works",

number = "2-3",

}

TY - JOUR

T1 - An Interval Newton Method

AU - Greenberg, R I.

AU - Hansen, Eldon R.

PY - 1983/5/1

Y1 - 1983/5/1

N2 - We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.

AB - We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.

KW - systems of nonlinear equations

UR - https://ecommons.luc.edu/cs_facpubs/91

U2 - 10.1016/0096-3003(83)90001-2

DO - 10.1016/0096-3003(83)90001-2

M3 - Article

VL - 12

JO - Computer Science: Faculty Publications and Other Works

JF - Computer Science: Faculty Publications and Other Works

IS - 2-3

ER -

An Interval Newton Method

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this