Directional Newton methods in n variables

Yuri Levin; Adi Ben-Israel

doi:10.1090/S0025-5718-01-01332-1

Directional Newton methods in n variables

Yuri Levin, Adi Ben-Israel

Rutgers Business School, Management & Information Systems

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

31 Scopus citations

Abstract

Directional Newton methods for functions f of n variables are shown to converge, under standard assumptions, to a solution of f(x) = 0. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of f with maximal modulus. These methods are applied to solving systems of equations without reversion of the Jacobian matrix.

Original language	English (US)
Pages (from-to)	251-262
Number of pages	12
Journal	Mathematics of Computation
Volume	71
Issue number	237
DOIs	https://doi.org/10.1090/S0025-5718-01-01332-1
State	Published - 2002

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

Keywords

Newton method
Single equations
Systems of equations

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10.1090/S0025-5718-01-01332-1

Cite this

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abstract = "Directional Newton methods for functions f of n variables are shown to converge, under standard assumptions, to a solution of f(x) = 0. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of f with maximal modulus. These methods are applied to solving systems of equations without reversion of the Jacobian matrix.",

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AU - Ben-Israel, Adi

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AB - Directional Newton methods for functions f of n variables are shown to converge, under standard assumptions, to a solution of f(x) = 0. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of f with maximal modulus. These methods are applied to solving systems of equations without reversion of the Jacobian matrix.

KW - Newton method

KW - Single equations

KW - Systems of equations

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DO - 10.1090/S0025-5718-01-01332-1

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VL - 71

SP - 251

EP - 262

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 237

ER -

Directional Newton methods in n variables

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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