Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms

Xiaojun Chen; Tetsuro Yamamoto

doi:10.1016/0377-0427(94)90036-1

Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms

Xiaojun Chen, Tetsuro Yamamoto

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

Abstract

In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally, a numerical example is given.

Original language	English
Pages (from-to)	311-324
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	55
Issue number	3
DOIs	https://doi.org/10.1016/0377-0427(94)90036-1
Publication status	Published - 30 Nov 1994
Externally published	Yes

Keywords

Convergence analysis
Moore-Penrose inverse
Newton-like methods
Nonlinear equations with nondifferentiable terms
Underdetermined systems

ASJC Scopus subject areas

Applied Mathematics
Computational Mathematics
Numerical Analysis

More information

10.1016/0377-0427(94)90036-1

Cite this

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abstract = "In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally, a numerical example is given.",

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N2 - In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally, a numerical example is given.

AB - In this paper we consider Newton-like methods for solving underdetermined systems of nonlinear equations with nondifferentiable terms. After presenting local convergence analysis for the methods, we prove a semilocal convergence theorem as well as uniqueness of solution in a generalized sense. Another semilocal convergence theorem for the Newton-chord method is also established. Finally, a numerical example is given.

KW - Convergence analysis

KW - Moore-Penrose inverse

KW - Newton-like methods

KW - Nonlinear equations with nondifferentiable terms

KW - Underdetermined systems

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DO - 10.1016/0377-0427(94)90036-1

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EP - 324

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

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ER -

Newton-like methods for solving underdetermined nonlinear equations with nondifferentiable terms

Abstract

Keywords

ASJC Scopus subject areas

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